Just another data point. I'm a lefty, left eye dominant. I tought myself how to shoot right-handed handguns because most handguns, especially back then, were made for the predominantly right-handed world. Although I still use my left dominant eye, just cock my head slightly, which probably isn't even noticable to an observer.
But when it comes to rifles I shoot lefty. It's too hard to break the left eye dominance.
Your son will likely be more abidextrous than most people.