I just tried the exercise you just mentioned...Now, I'm right handed all the way, the only thing I can do with my left hand is punch. But when I stand on my right leg, closing either eye, I wobble all over the place. If I stand on my left leg, with my right eye open, I am real solid. Slightly less so standing on my left leg with the left eye open. What is happening there?
For what it is worth, I shoot equally well with either hand, but, when I shoot right handed, with a pistol, I arrange myself so my left eye does most of the seeing.