I always just shut one eye, never taught anything else so I just went with what was comfortable. Works with sporting clays but I struggle a bit with a pistol.
Well, in the movie "American Sniper", Chris Kyle keeps both eyes open "to see the whole battlefield". I have no idea if that is based on fact, but it is how an army shooter taught me to aim. I keep both eyes open. It is less stressful when peering through a scope for long periods of time.