Can I set up a Driver for the bone on the left to slightly copy the rotation of the selected one when rotating clockwise on its Z axis, and to copy the rotation with higher influence when rotated counter clockwise on its Z axis?
you could do this by putting a simple condition in your driver's code block:
zrot / 2 if zrot < 0 else zrot * 5
which gives this:
⚠️ Note that you can just map the range(-180,180) to something else. it means that if you rotate counterclockwise when zRotation is currently greater than zero this doesn't work. if that's what you really need you can animate your reference bones and using f-curves you can do the rest.