I'd like to suggest that if you have access to a left handed rifle that you give that one a try with both the left and the right eyes to determine which eye you shoot better with. I for one "cannot" shoot with both eyes open, I've tried it and just not going to happen for me!! My thoughts are that "dominant eye" determination is done by the autonomic nervous system of the body; meaning the body is "hardwired" and something that you have no control over how it works. With that said, you do have control over how the bolt of your rifle is moved and how you shoulder the rifle. Again try shooting the left handed rifle left handed and see which hand you shoot best with.