I am right hand dominant and left eye dominant. Didn’t know it until I was in my mid twenties when I was having a real bad issue with missing when bird hunting. Also the same season I switched to a different gun. I grew up working at a trap and skeet club. From 12-18. So I have shot many many thousands of rounds out of a shotgun.
What I have found is that there is a bit of a learning curve between different weapons. Slight adjustments make a big difference.
Shotguns- fit of the gun makes such a big difference. I will go from a very above average shotgun shooter to the laughing stock of a bird hunt, if I switch up guns. I can not try my buddies guns, because I cannot rely on the bead to be where the gun is actually aiming. I shoot benellis, they have shim adjustments in the box when you buy a new one. I take gun out and set up 3 pieces of paper at 30ish yards across a sheet of plywood. Pull bead off gun and then shoot shots at the paper as fast as I can. Then I switch up shims until I find a combination I like. I use the ammo and choke I hunt with.
Bow hunting- I switched up to a single pin, which was a huge help. But my main fix here is I blink my left eye and watch to see what set of pins disappears. It’s the right side all the time. But by blinking my brain can remember that it is the correct set of pins to shoot with. Super simple fix there, and it does nothing to shot sequence.
Pistols- By far the hardest, and my least practiced firearm. On this I know what I do is wrong But I hardly shoot pistols. This one I just close an eye. Not the same one everytime. Still trying to figure out what works best for me. And then I manipulate the gun to match which eye I want open on a given day.
Rifles- By far the easiest. Aquire the target with both eyes open. Once safety comes off I close my left eye.
Hope any of this helps. Keep working at it with ur boy. He will get it Worst they will happen is you have to spend more time shooting guns and hanging out.