If you're closing the dominant eye then it doesn't matter. You are only going to see out of the eye that's open. So if you're using a peep and pins it's a moot point. If you are shooting traditional with both eyes open or a shotgun for example then you should shoot with your dominant eye on the barrel/ arrow etc.
I trained alot of young marksmen back in the day and we used to put eye patches on them. They shot just fine and learned to shoot with the off eye closed. No dominance issues.
Thank you sir, im left eye dominant but shoot right handed, when i first started shooting a bow i would wear an eye patch, now i shoot just fine right handed without the patch. close the left eye and line up the pin through the peep and it doesn't matter.
good thread op