I shoot right handed. Both right and left eyes are too close in dominance to each other so I must close one when deliberately shooting a rifle.
When shooting a pelter, I keep both eyes open and only look at the intended target. I don't even see the end of the barrel, except when shooting a flintlock pelter - then left eye closed and deliberate lead and pull.
With iron sights (or scope) and both eyes open, my dominance changes, right/left/right/left/right/left- objects - ie; sights and target jumping left and right, bakc and forth- must close left eye when shooting right handed, right eye when shooting left handed.
The only time I don't do this in deliberate fire, is with metalics in prone - then I use both eyes open and a blinder over the left eye, so only the right eye cans see the sights and target. Having both eyes open helps reduce fatigue in the eyes.