The electronic structure, geometry and energetics of Ga vacancy pairs and N vacancy pairs in both wurtzite and zincblende GaN are investigated via molecular dynamics (MD) simulations using an empirical tight-binding (TB) model with total energy capabilities and supercells containing up to 216 atoms. Our calculations suggest that, by pairing, N vacancies, which in isolation act as shallow donors, can lower their collective formation energy by about 5 eV. In doing so, however, these N vacancies lose their shallow-donor character as the lattice relaxes in response to this aggregation. Contrasting with the N vacancies, the Ga vacancies are found to retain their isolated shallow acceptor behavior and do not gain significant energy upon aggregation. The possible implications for larger aggregate defects are discussed.