Just magnets. Really strong neo-magnets? So when they are near, they join, but can be split by a normal strength person to use them independently.
What's to stop them from catching during independent use? Seems like a hiccup with that would mess with gameplay. Maybe electromagnets... that way there would be no extra moving parts, but again, would have to be under current the whole time and could potentially burn out.
I gave a fair amount of thought to using a magnetic AC compressor clutch for a 360/270 degree steering wheel project.

Plenty strong enough, but they pull a LOT of current. I was also afraid that having that strong of a magnet near the monitor/computer/user might lead to other issues.
Attached is my entry for worst drawing in paint.
I left some stuff out to keep it from looking too complicated.
The actuator would attach to the right axle. The point where it attaches to the middle part would slip, so it doesn't push the center part, but just allows the spring to move it.
There would be a plate on the end of the middle part keyed in such a way that the left axle could only go in when they are lined up.
If the axles have less than 90 degrees of rotation, this might not even be a problem as there would only be one point where the two square pieces could slip together.