I am left-eyed dominant and right-handed and have been shooting since I was a small boy. Never really thought about it being something I had to learn, but shooting rifle I shoot right handed and close my left eye.

Shooting handgun is a little different. I still use my right hand, but sometimes squench my left (dominant) eye and sight with right, and sometimes slightly angle my grip and use left eye to sight. Seem to do both and don't usually notice which way I'm doing it unless I think about it.

Whatever way you decide to do, do it enough to make it natural.