Try learning both ways-i.e. try shooting left handed, and try shooting right eyed...whichever works better is the way to go.

I'm pretty well ambidexterous, and focus equally well with both eyes, but when it comes down to shooting, I'm all over the place...I shoot long guns right handed, right eyed, I shoot most handguns either hand, but usually shoot better left handed...I also shoot Gunfighter in CAS/SASS, which means I shoot two pistols simultaneously, I usually focus with my left eye for both hands-although I don't use my sights much. I'm a better clay shooter left handed too, for some reason it just feels better to shoulder a SxS lefty. I can't shoot a lever action very well left handed, except for SHORT bbl versions.

When it comes to semiauto pistols that have a safety or some other function that lends itself to right handed shooting, I usually shoot them right handed, and I almost always shoot double action revolvers right handed (because reloading a double action in your right hand isn't really "handy"-no pun intended).

I've pretty much always been this way, but doing anything well takes work.