When neither eye is dominant, both can be used together, or individually. People with a very dominant eye are better off shooting from that shoulder, and one-eyed. People who's dominant eye is strongly dominant find it harder to shoot with both eyes open, leading to 'cross-firing'. (I am referring more to wing shooting, or clays games.) When I was a 4-H Shooting Sports Leader, no matter the discipline, the first thing we did at orientation was determine each kid's dominant eye, if they had one. More girls do not have one, but some guys didn't either, and some girls did have one. We'd then recommend to the parents a gun or bow in that hand. (we had some LH bows for the kids to try.) Some had already been shooting RH, but were left eye dominant. (In my case about 50 years now.) The sooner they'd switch, usually, the faster they'd improve. (I do shoot off of both shoulders, and could shoot a bow either hand, before my left arm had some nerve damage, though I am better right handed, even though I'm left eye dominant, simply because I've shot that way for over 50 years)
We'd advise the kids who didn't have a dominant eye, or only slight dominance, to choose whichever shoulder felt more comfortable to shoot off of, (or which hand for bow). As for advising all the kids to at least try to shoot off the other shoulder (or other handed bow) once in a while is as I mentioned, it comes in handy; either hunting, self defense, or in military or Law Enforcement service.