I let my 9 year old do things last March like, go to the bathroom, or get a drink refill, walk over to a different food stand, (where he was in shouting distance). He asked me how old he would need to be for him to do things on his own, and I told him maybe 13? I know I was about 11 or 12 when my parents let me go off for an hour or two at DL, but that was 20+ years ago. My oldest is MEGA responsible (he will be 10 in a few weeks), but still. It's other people that scare me. We're going next summer for 10 days, I can see myself letting him say, browse the Japanese merchantile while we're getting lunch at the counter service place in Japan, or let him go on a ride on his own if we're at the exit, let him spread his wings a bit, but not on his own.
Anyway, I think 13 or so would be an appropriate age, esp with a sibling, cell phone and just a few hours, not the whole day.