We investigate the spin-resolved electronic structure of native vacancies and substitutional defects in monolayer GaS and GaSe using an anisotropic screened-exchange functional developed for two-dimensional material systems. By combining an energy-based classification of defect-associated states with spatially resolved projections and partial charge densities, we examine how these defects modify the in-gap electronic structure and assess their relevance for defect-based single-photon emission. The results identify gallium vacancies, particularly in GaS, as candidates single-photon emitters.