I've been helping out at a class for shotgun instructors as a sort of practice student. One of the things the would be instructors do is test eye dominance. The first test is for me, when instructed, to point at the instructor's right eye with my right hand index finger (I'm left handed). I was quickly diagnosed as strongly right eye dominant. A little later we go on to a similar check but using an unloaded (!) shotgun instead of my index finger. Shock horror, I was immediately seen to be strongly left eye dominant. There followed much discussion on this apparently unusual situation before decamping to the shooting ground to be further instructed.
No wonder I'm such a lousy shot.