I'm right handed, left eye dominant. I've tried both eyes open which was problematic under stress, and tape on the left lens which made reloads more difficult. Now I just close my left eye, and open it for movement and reloads.
After a year of that, my right eye is becoming more dominant - I randomly use either eye on dominance tests now. Although, trying to use my left eye on WHO screwed me up for awhile again.