If both the captor and the captive play the same game, the captive will have the advantage since he doesn't need to split his attention. All he does is playing the minigame. The captors should have such an advantage that he will be able to both lead the captive and remain with an advantage in the minigame.

I was thinking about a minigame like this:
There is a big hollow circle and a small solid circle inside it. The captor can spin the big circle, and the captive can move the smaller circle. The big circle has several gates - parts of the circle that are missing. If the captive can get his small circle out of the big circle thro one of the gates - he can break free.

I also thought of a version for the consciousness regaining situation - In this version, the samll circle is invisible to the captor, but if the small circle touches the big circle, the captor will notice it and the small circle will go wild until the captive can regain controll on it.

The difficulty of both minigames depends on the size of the circle, the size of the gates, and on the speed and acceleration of the spinning of the big circle and the movement of the small ones. Those values can be changed via trial and error to reach the desired results.