In my case, right handed/left handed dominant, I shoot PISTOL right handed with no problem. I move the pistol a little bit towards my dominant eye(left) until I find " the right spot."
Now LONG GUNS, I shoot left handed. At the end you have to find what best works for you. It is a combination of adapting your body and training, which plays an important part. For me is a natural thing after doing it for so long. Time will tell which position is the best.