I believe Jeff Cooper was cross dominant, so it is by no means unusual or will prevent you from shooting well. As prolific a writer as he was, I expect you can do a search including his name for some examples and information. Generally speaking with handguns (given many folks' use for defensive/tactical shooting disciplines) leaving both eyes open but having the head cocked to the side to align the eyes is the basic idea. In bullseye, it is more likely acceptable to either use a dominant eye blinder or a pair of shooting glasses with a blacked out eye, especially while retraining your eyes. Overcoming a lifetime of using the other eye (and the natural dominance of it) may take plenty of practice but it's definitely possible. I'm on a mobile device ATM which makes it a bit slower to pull links, but I'll happily post some reference material later in the day on this topic if its not already been answered in depth by then.
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