Irradiation of GaN by 2.5-MeV electrons in situ at 4.2 K produces a broad photoluminescence (PL) band centered at 0.95 eV. Optical detection of electron paramagnetic resonance (ODEPR) in the band reveals two very similar, but distinct, signals, L5 and L6, which we identify as interstitial ${\mathrm{Ga}}^{2+}$ in two different lattice configurations. L5, present immediately after the irradiation, is seen via a spin-dependent electron transfer process from the shallow effective-mass donor (EM) which competes with the PL (negative signal). L6 emerges upon annealing at various stages starting at $\ensuremath{\sim}60\mathrm{K},$ possibly assisted by optical excitation, as a spin-feeding process (positive signal) not involving the EM donor. Both L5 and L6 disappear upon prolonged annealing at room temperature, with L6 disappearing first. Most of the 0.95-eV band $(\ensuremath{\sim}85%)$ also disappears in this anneal, the remaining fraction being stable to $\ensuremath{\sim}500\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}.$ Two tentative models are presented, each of which identifies L5 and L6 with ${\mathrm{Ga}}^{2+}$ in different interstitial sites near the gallium vacancy from which they were created. Both models ascribe the 0.95-eV PL band, along with an ODEPR signal observed in it L1 as arising from the Ga vacancy, which in its isolated form is therefore stable to $\ensuremath{\sim}500\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}.$
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