Oxygen is the most common unintentional impurity found in GaN. We study the interaction between substitutional oxygen (ON) and the gallium vacancy (VGa) to form a point defect complex in GaN. The formation energy of the gallium vacancy is largely reduced in n-type GaN by complexing with oxygen, while thermodynamic and optical transition levels remain within the bandgap. We study the spectroscopy of this complex using a hybrid quantum-mechanical molecular-mechanical embedded-cluster approach. We reveal how a single defect center can be responsible for multiband luminescence, including possible contributions to the ubiquitous yellow luminescence signatures observed in n-type GaN, owing to the coexistence of diffuse (extended) and compact (localized) holes.