No boys my kids are generally well behaved .... in my daughter's words...."Don't worry mommy I am only naughty with you or grammy." I have never had a teacher say they did behave appropriately in school. They are smart enough to know when they can fool around and when they need to listen to rules.
There wasn't a sign like I have seen at say hotel pools, it isn't a true public pool as in a community pool, but a Y outdoor center with 3 pools where you are supposed to be a member or a guest of a member. 2 girls were 12 and the other two were 16 and 14. With the 16 in charge. I gave specific instructions if the younger ones fooled around I was to be called and I'd come get them.
I just have seen some notices like at hotels that say you have to be a certain age or above or with an adult over 18. But these typically do not a life guard.
They do have an overall gym rule where if you are under 13 you are supposed to be within the Y (not necessarily right where your kid is). My daughter is also just a month shy of 13. And all are very good swimmers - just know personally it doesn't matter how good you are if you slip or something like that. And no one is right there to see it. My uncle did and he swam all the time, almost drown, but his adult son showed up, unfortunately he ended up paralyzed.