I write left handed. I shoot pistol mostly right handed, left eye dominant 99.9% of the time. I also shoot (for example, when shooting around cover) right hand, right eye, then easily switch off when changing sides to my support hand and shoot left hand, left eye dominant. It took some training to get on sight and accurate with my right eye but now it's an either/or for me as the situation dictates. (Also if I don't put my hair up or wear a hat and my hair blows in my face, I can easier adapt what eye has a clear shot rather than wasting time trying to battle with all of my hair. I know in a SD situation, chances are, my hair will be down and the BG won't wait for me to get my hair out of my face to clear my dominant eye).
For rifle, I shoot right side, right eye. (I have a Tavor and would rather not eat my brass trying to shoot it without the lefty conversion kit).