I was right eye dominant, right handed. My optic nerve was cut during a surgery. I can’t make tears and have really blurry, cloudy vision in it. I shoot split vision and to be honest I don’t feel handicapped being I don’t truly aim.
You’ll not need to cover your eye if it’s not dominant anymore. That’s why you cover an eye to force dominance to switch and you don’t notice a reaction. Remember you don’t cover it to throw garbage in the trash, step off a curb, jump a brook, etc. your eye naturally does it. Don’t sweat it too hard and don’t over analyze it