Or simply close the eye. I am cross or switch dominance to some extent, that is, I shoot right handed, but if I keep both eyes open, my left will take over dominance, then switch back to right eye dominance, which means I'm looking down the sights, very weakly though, then I'm looking at the side of the rifle, then the sights again, then the side of the rife again. The inability to shoot both eyes (due to the eyes switching Dominance)open except for with a shotgun had been with me since I was a kid. I simply close the left eye when shooting right handed, and the right eye when shooting left handed. Both eyes are open when shooting birds as I don't see the barrel, only the bird.