I am right handed and left eye dominant. Using my right eye is not an option. That is because I was born with bilateral crossed eyes (strabismus). Back in the early 1960's, the state of the art was to not perform eye muscle surgery until the child was six years old or so. This led to the infant brain learning to suppress the vision in one eye, which is called amblyopia. This happened to me. Consequently, my right eye vision is so poor, I cannot see sufficiently well to drive, read or shoot out of that eye. If anything happened to my left eye, I would be essentially blind for all intents and purposes. Nowadays, children born with strabismus have the surgery at one or two weeks of age just to avoid amblyopia.
I shoot long guns left handed and with handguns use a Weaver stance at arm's length with my head canted over to use my left eye. If I am not paying attention, my groups will be low and to the left, which several instructors have told me is a function of my cross dominance.