You know that it’s harder to balance when you close your eyes. The question is why?
We know that the optic nerve sends signals to the brain, that’s how we see. So if you look at the optic nerve as a current-carrying wire, it would produce a magnetic field. And where two magnetic fields overlap, there is a resultant force.
In this case, when currents flow in the same direction, the magnetic force is inward. And I believe that this resultant force is a portion of what we use for balance. If you close your eyes, you have no [or significantly less] information to send from the optic nerve to the brain. This would reduce the current, and thus reduce the strength of the magnetic field.