Is there really anything one can do to expedite vanquishing or neutralizing a victim in an incapacitated condition from Hypnotic Gaze?
The Wizard School of Enchantment gives the skill Hypnotic Gaze at 2nd level which leaves a creature that fails its save with the condition incapacitated. Incapacitated means the creature cannot take actions or reactions. Damage ends the effect.
Theoretically, using the reaction action, all damage from multiple PCs could be delivered at one time - but those attacks are not at advantage or auto-critical because incapacitated doesn’t mean paralyzed.
Though attaching manacles might seem to be one option or throwing the creatures weapon away so it is unavailable could be another - both apparently could be resisted by an incapacitated victim as noted by the first answer below.
What are other viable combat actions that could be used to optimally increase the chances of dispatching an opponent with the incapacitated condition?
Of note — this is not a duplicate of How does one dispatch a helpless opponent?. None of the answers in that question apply. Paralyzed & unconscious creatures (which that question addresses) and sleeping creatures (which that question addresses) are not the same as incapacitated. Incapacitated simply means the creature cannot take actions or reactions. Attacks don’t have advantage and hits aren’t automatic criticals like with paralyzed or unconscious victims. The creature isn’t helpless when incapacitated - despite the typical real world meaning of the word. Lastly and most importantly, paralyzed and unconscious conditions don’t end with damage like the condition does with hypotic gaze which changes the possible actions. These are different questions requiring different answers.