I'm sorry that your son didn't get in. You should definitely appeal, especially since your school is encouraging you to appeal. Unfortunately, that requires some "new" piece of information, so you'll probably need to contact George Mason University and pay for a WISC test (or do it through a private tester that meets Fairfax County's criteria).
My impression is that a 13 is a fine GBRS score, and that shouldn't have kept him out. Were his Cogat scores really inconsistent with his NNAT score? If so, that may have concerned the eligibility committee, and a good WISC score might result in his being declared eligible. Good luck.