You're looking at this the wrong way
From one point of view, your understanding of how horses are controlled is completely correct. From another, it's completely in error. The problem is that you don't appear to understand what's happening.
What the rider is doing is training the animal. In the beginning (especially if done badly), a form of coercion is used — the bit in the mouth that drags the horses head into the direction the rider wants. But the bit isn't enough to exert total control. How do you cause a gallop, for instance (coercion: spurs)?
What any good animal trainer (including those of horses) will tell you that the animal will be under better control if rewarded for behaving as desired. Thus, if the method of control you want to use is a bitless bridle, then all you need is patience, affection, and a lot of apples or sugar cubes. If you don't want to to take that much time, the bit is faster, but the bond (I believe) is weaker. With a dragon, that might have somewhat irreversible consequences.
My point is, what "method" you use for control (bridle, knee pressure, vocal commands, slapping/tapping with a crop, etc.) is an aesthetic. It's window dressing (kinda, I'll talk about this momentarily). What counts is that the creature has been trained to behave in a specific way as directed by a desired method, and from a certain point of view, no method is better than another.
Like I said... kinda...
One of the evidences of the masterpiece that is Dune is the control of sand worms. We're talking about creatures that have one or more attributes that doesn't allow them to be trained like, for instance, a dog or a monkey. They're huge! They're mindless! There isn't an apple importable in the galaxy that would impress them! Herbert created a creature that had to be coerced (and subjugation of nature being one of the themes of his books...). How did he describe it? Methods were used to open a seam along the body that let irritating sand into soft subdermal skin, causing the worm to roll, which caused the worm to turn. The order in which tools were used to expose that soft flesh determined the direction of the roll.
And, of course, there were those at the tail of the worm slapping the snot out of it to make it go faster. In some ways, humanity never changes.
So... what attributes or characteristics about your dragon would lead to a unique method for conveying directions to the trained creature? Nerve clusters? Irritated muscles? Electric shock?
Because the method is window dressing (like asking what color you should paint a house), a question about what methods could be used is inappropriate on this Stack. They're all equally valid and depend solely on your design of your creature — but the answer to this present question is simply this:
Train your dragon.