Sauron could not read Tom Bombadil’s mind without Tom’s permission, palantír or no palantír. In fact, he could not read anyone’s mind without their permission.
Tolkien explains what we would call telepathy as ‘sanwe’, communication from mind to mind.
Pengolodh says that all minds (sáma, pl. sámar) are equal in status, though they differ in capacity and strength. A mind by its nature perceives another mind directly. But it cannot perceive more than the existence of another mind (as something other than itself, though of the same order) except by the will of both parties. The degree of will, however, need not be the same in both parties. If we call one mind G (for guest or comer) and the other H (for host or receiver), then G must have full intention to inspect H or to inform it. But knowledge may be gained or imparted by G, even when H is not seeking or intending to impart or to learn: the act of G will be effective, if H is simply “open” (láta; látie “openness”). This distinction, he says, is of the greatest importance.
— “Ósanwe-kenta”, in Vinyar Tengwar, July 1998.
Tolkien goes into some detail describing the logistics and limitations of sanwe. For example, distance is no obstruction, but the sanwe can be strengthened by such things as urgency, affinity, or authority. But regardless, it can never take place without the consent of both parties, which cannot be extorted by force.
Though in “Arda Unmarred” openness is the normal state, every mind has, from its first making as an individual, the right to close; and it has absolute power to make this effective by will. Nothing can penetrate the barrier of Unwill.
All these things, says Pengolodh, are true of all minds, from the Ainur in the presence of Eru, or the great Valar such as Manwë and Melkor, to the Maiar in Eä, and down to the least of the Mirröanwi.
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In like manner, extortion of the secrets of a mind may seem to come from reading it by force in despite of its unwill, for the knowledge gained may at times appear to be as complete as any that could be obtained. Nonetheless it does not come from penetration of the barrier of unwill.
There is indeed no axan that the barrier should not be forced, for it is únat, a thing impossible to be or to be done, and the greater the force exerted, the greater the resistance of the unwill. But it is an axan universal that none shall directly by force or indirectly by fraud take from another what he has a right to hold and keep as his own.
Melkor repudiated all axani. He would also abolish (for himself) all únati if he could. Indeed in his beginning and the days of his great might the most ruinous of his violences came from his endeavour so to order Eä that there were no limits or obstacles to his will. But this he could not do. The únati remained, a perpetual reminder of the existence of Eru and His invincibility, a reminder also of the co-existence with himself of other beings (equal in descent if not in power) impregnable by force. From this proceeds his unceasing and unappeasable rage.
He found that the open approach of a sáma of power and great force of will was felt by a lesser sáma as an immense pressure, accompanied by fear. To dominate by weight of power and fear was his delight; but in this case he found them unavailing: fear closed the door faster. Therefore he tried deceit and stealth.
— “Ósanwe-kenta”, in Vinyar Tengwar, July 1998.
In this case, ‘deceit and stealth’ meant that Melkor had to convince people he was trustworthy and their friend before he could read their mind - not an easy task! He could never do it by force. Indeed, it came out that language was a great help to Melkor:
Therefore he sought means to circumvent the únat and the unwill. And this weapon he found in “language”. For we speak now of the Incarnate, the Eruhíni whom he most desired to subjugate in Eru’s despite. Their bodies being of Eä are subject to force; and their spirits, being united to their bodies in love and solicitude, are subject to fear on their behalf. And their language, though it comes from the spirit or mind, operates through and with the body: it is not the sáma nor its sanwe, but it may express the sanwe in its mode and according to its capacity. Upon the body and upon the indweller, therefore, such pressure and such fear may be exerted that the incarnate person may be forced to speak.
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Thus by deceit, by lies, by torment of the body and the spirit, by the threat of torment to others well loved, or by the sheer terror of his presence, Melkor ever sought to force the Incarnate that fell into his power, or came within his reach, to speak and to tell him all that he would know. But his own Lie begot an endless progeny of lies.
— “Ósanwe-kenta”, in Vinyar Tengwar, July 1998.
So even Morgoth, at the height of his power, could not read another’s mind without their free and open consent. It is an ironclad law of the physics of Middle-Earth. If Morgoth at his height could not, surely Sauron in the Third Age could not, palantír or no palantír!
Tolkien goes on about the palantír at some length in Unfinished Tales, and indeed, the Stones only seem to make sanwe easier for peoples not accustomed to it. Mind-reading, as you’d expect from Tolkien’s statements above, still requires the consent of both parties.
The palantíri could not themselves survey men’s minds, at unawares or unwilling; for the transference of thought depended on the wills of the user on either side, and thought (received as speech) was only transmittable by one Stone to another in accord.
— Unfinished Tales, Part Four, “The Palantíri”.
The ‘thought’ received as speech is not quite normal sanwe, though:
In a detached note this aspect is more explicitly described: ‘Two persons, each using a Stone “in accord” with the other, could converse, but not by sound, which the Stones did not transmit. Looking one at the other they would exchange “thought” — not their full or true thought, or their intentions, but “silent speech”, the thoughts they wished to transmit (already formalized in linguistic form in their minds or actually spoken aloud), which would be received by their respondents and of course immediately transformed into “speech”, and only reportable as such.
— Unfinished Tales, Part Four, “The Palantíri”.
We have four examples of people using the palantír and facing Sauron, and he was not able to read any of their minds. Even Pippin is forced to speak (terrified into speaking by Sauron’s presence) rather than having his mind read. In fact, Sauron is completely mistaken about Pippin’s story and circumstances! He learns nothing of value from the interaction.
‘I did not answer. He said: “Who are you?” I still did not answer, but it hurt me horribly; and he pressed me, so I said: “A hobbit.”
‘Then suddenly he seemed to see me, and he laughed at me. It was cruel. It was like being stabbed with knives. I struggled. But he said: “Wait a moment! We shall meet again soon. Tell Saruman that this dainty is not for him. I will send for it at once. Do you understand? Say just that!”
‘Then he gloated over me. I felt I was falling to pieces. No, no! I can’t say any more. I don’t remember anything else.’
— The Lord of the Rings, Book Three, Chapter XI, “The Palantír”.
Pippin feels ‘forced to speak’, but Sauron gathers nothing other than what Pippin says, which is not even an actual answer to his question! In fact, he wants Pippin brought to him in person, so he can interrogate him through torture — hardly a sensible step if he could glean all he needed to know through the palantír. And this should remind us that Gollum, too, had to be interrogated through torture, and not through other means.
Sauron was unable to do anything to Denethor, except control to some degree what Denethor could see through the Stone.
‘Though the Stewards deemed that it was a secret kept only by themselves, long ago I guessed that here in the White Tower, one at least of the Seven Seeing Stones was preserved. In the days of his wisdom Denethor did not presume to use it, nor to challenge Sauron, knowing the limits of his own strength. But his wisdom failed; and I fear that as the peril of his realm grew he looked in the Stone and was deceived: far too often, I guess, since Boromir departed. He was too great to be subdued to the will of the Dark Power, he saw nonetheless only those things which that Power permitted him to see. The knowledge which he obtained was, doubtless, often of service to him; yet the vision of the great might of Mordor that was shown to him fed the despair of his heart until it overthrew his mind.’
— The Lord of the Rings, Book Five, Chapter VII, “The Pyre of Denethor”.
According to Tolkien, Denethor actually used the palantír from almost the moment he had access to it, and actually had much more freedom of the stone than Gandalf suggests. At any rate, he was certainly not mind-read or controlled by Sauron:
Gandalf might well think as he did on the matter, but it is probable, considering Denethor and what is said about him, that he began to use the Anor-stone many years before 3019, and earlier than Saruman ventured or thought it useful to use the Stone of Orthanc. Denethor succeeded to the Stewardship in 2984, being then fifty-four years old: a masterful man, both wise and learned beyond the measure of those days, and strong-willed, confident in his own powers, and dauntless. His ‘grimness’ was first observable to others after his wife Finduilas died in 2988, but it seems fairly plain that he had at once turned to the Stone as soon as he came to power, having long studied the matter of the palantíri and the traditions regarding them and their use preserved in the special archives of the Stewards, available beside the Ruling Steward only to his heir. ... Confrontation with Sauron almost certainly did not occur for many years, and was probably never originally contemplated by Denethor. Denethor could, after he had acquired the skill, learn much of distant events by the use of the Anor-stone alone, and even after Sauron became aware of his operations he could still do so, as long as he retained the strength to control his Stone to his own purposes, in spite of Sauron’s attempt to ‘wrench’ the Anor-stone always towards himself. It must also be considered that the Stones were only a small item in Sauron’s vast designs and operations: a means of dominating and deluding two of his opponents, but he would not (and could not) have the Ithil-stone under perpetual observation. It was not his way to commit such instruments to the use of subordinates; nor had he any servant whose mental powers were superior to Saruman’s or even Denethor’s. ... Sauron failed to dominate him and could only influence him by deceits.
— Unfinished Tales, Part Four, “The Palantíri”.
And similarly, Aragorn was not mind-read through the palantír. In fact, Sauron made an enormous error in his encounter with Aragorn - he assumed Aragorn had the Ring, and accelerated his war-plans, which led to the defeat at Pelennor and ultimately to Sauron’s total defeat, since he was straining to look at everything Aragorn was doing rather than paying attention to his own backyard.
‘You forget to whom you speak,’ said Aragorn sternly, and his eyes glinted. ‘Did I not openly proclaim my title before the doors of Edoras? What do you fear that I should say to him? Nay, Gimli,’ he said in a softer voice, and the grimness left his face, and he looked like one who has laboured in sleepless pain for many nights. ‘Nay, my friends, I am the lawful master of the Stone, and I had both the right and the strength to use it, or so I judged. The right cannot be doubted. The strength was enough - barely.’
He drew a deep breath. ‘It was a bitter struggle, and the weariness is slow to pass. I spoke no word to him, and in the end I wrenched the Stone to my own will. That alone he will find hard to endure. And he beheld me. Yes, Master Gimli, he saw me, but in other guise than you see me here. If that will aid him, then I have done ill. But I do not think so. To know that I lived and walked the earth was a blow to his heart, I deem; for he knew it not till now. The eyes in Orthanc did not see through the armour of Théoden; but Sauron has not forgotten Isildur and the sword of Elendil. Now in the very hour of his great designs the heir of Isildur and the Sword are revealed; for l showed the blade re-forged to him. He is not so mighty yet that he is above fear; nay, doubt ever gnaws him.’
— The Lord of the Rings, Book Three, Chapter XI, “The Palantír”.
Even though Saruman was under Sauron’s sway, as it were, it’s clear that Saruman’s mind was not laid bare to Sauron: else his treachery would have been detected many years earlier; he has only been persuaded and daunted.
‘Easy it is now to guess how quickly the roving eye of Saruman was trapped and held; and how ever since he has been persuaded from afar, and daunted when persuasion would not serve. The biter bit, the hawk under the eagle’s foot, the spider in a steel web! How long, I wonder, has he been constrained to come often to his glass for inspection and instruction, and the Orthanc-stone so bent towards Barad-dûr that, if any save a will of adamant now looks into it, it will bear his mind and sight swiftly thither? (Saruman)
So, let us instead consider the question of whether or not Sauron could daunt Tom, terrify him into speaking. He could not do so to Denethor or to Aragorn, but what about Tom? Let’s see how Tom faces down immortal horrors:
Tom stooped, removed his hat, and came into the dark chamber, singing:
Get out, you old Wight! Vanish in the sunlight!
Shrivel like the cold mist, like the winds go wailing,
Out into the barren lands far beyond the mountains!
Come never here again! Leave your barrow empty!
Lost and forgotten be, darker than the darkness,
Where gates stand for ever shut, till the world is mended.
At these words there was a cry and part of the inner end of the chamber fell in with a crash. Then there was a long trailing shriek, fading away into an unguessable distance; and after that silence.
— The Lord of the Rings, Book One, Chapter VIII, “Fog on the Barrow-downs”.
or, Tom, when faced with the malign influence and power of the Ring:
Tom laughed again, and then he spun the Ring in the air - and it vanished with a flash. Frodo gave a cry - and Tom leaned forward and handed it back to him with a smile.
— The Lord of the Rings, Book One, Chapter VIII, “Fog on the Barrow-downs”.
Or, in the words of Goldberry:
Tom Bombadil is the Master. No one has ever caught old Tom walking in the forest, wading in the water, leaping on the hill-tops under light and shadow. He has no fear. Tom Bombadil is master.’
— The Lord of the Rings, Book One, Chapter VII, “In the House of Tom Bombadil”.
So Sauron certainly cannot read Tom Bomabil’s mind without his freely given consent, palantír or no palantír, and I think it’s safe to say, that, through the palantír, Sauron doesn’t stand a chance of daunting Tom Bombadil into speaking up and spilling whatever secrets he has.
