TUFFCUFF would be most appropriate for his age.
As far as your question about throwing, it really depends on how much throwing he’s done throughout the year up to this point. If he’s thrown/pitched consistently every week since early Spring, then it’s beneficial to take 2-3 months off at the end of the season to allow the arm time to rest. You can still focus on increasing strength and flexibility.
But if he didn’t play a lot during the season or if he hasn’t thrown consistently, then I’d take off a shorter amount of time.