Just an opinion but I've always been right eye dominant. I trained shooting pistol for years using both left and right hand, left or right eye, both eyes open. Shooting around corners is a lot safer that way.

May be easier with pistol because you focus on the front sight and the target is just a blur. I got so after awhile I could consciously change the focus from the front sight to the target and back again in a fraction of a second.

Try focusing on the front sight and see what happens. If it works for you then play with it a little. Brain training.

I'm retraining right now, had cataracts surgery and my new lenses don't focus well. I still shoot everything both eyes open, but I'm having to relearn.

IMO messing with what comes naturally to you can take you down a path that my be wrong for you. If it ain't broke don't fix it.

IMO I wouldn't try to move my rifle to my dominant eye, I'd try to train the non dominant eye to conform to my strong side.

My wife always looks funny sighting with her left eye, with the shotgun on her right shoulder, works for her I haven't tried to change it any. She shoots a pistol the same way.