I think the other tricky part is that gifted kids need lots of stimulation, intellectually and since other people are complex and potential sources of information that the drive for intellectual stimulation can confound. However, it is pretty well studied that extravert/introvert is one of the strongest "fixed traits."
DS is definitely an extravert and freaks a bit if he doesn't have frequent presence of others. I'm an introvert and this creates a tension between us.
If age peers aren't cutting it, the extravert will spend recess time chatting with a teacher or any adult they can find.