Your kid, your call. I would expect a 13yo who has demonstrated control of himself and dedication to safety to be OK.
When I was a kid getting to go deer hunting was when we were big enough to handle getting kicked by a gun that used buckshot. About 8 for most of us. There was no sitting with Dad watching over. They stuck us out well away from anyone else. Of course, most of us went squirrel hunting by ourselves at that age. Kids back then matured faster because they spent more time figuring things out on their own without parents hovering around telling them what not to do.
