I tried, many times, to shoot with both eyes open, over the years. I saw the side of the barrel. Trying it, now, the difference in vision between the two eyes is so great that I see 3 or 4 barrels, and at least one of them is blurry.
There is a constant, floating blur in the left eye since the retina reattachment. But, I do know I tried that enough times over the years that it wasnt going to work for me. Some people are strongly left or right handed, some are ambidextrous, and perhaps that happens with eye dominance, as well.

Best,
Ted