While every ballplayer is different and you should take into account how long the ballplayer’s season was (Feb-Aug for most), 8-10 weeks off from throwing is a good range for a 13-year old. The Fall is the time to really focus on an off-season strength & conditioning program. This program should focus on building strength in the legs, torso, back, and scapular stabilizers. Get plenty of soft tissue work (foam rolling) and don’t ignore flexibility and mobility work. The return on investment here will be huge when the player does pick the ball back up to start an off-season throwing program, usually right around now (late-October to early November).
We are nearing that 8-10 week range, but because this particular player played until the end of August, maybe wait until November to pick the ball back up.