Spin-lattice relaxation (SLR) of quadrupole nuclei in solids is due to several mechanisms. The "crystalline" quadrupole mechanism is related to the interaction of nuclear quadrupole moments with dynamic gradients of electric fields caused by modulation of the interatomic distances by thermal phonons. In real materials, which have both native paramagnetic defects and paramagnetic impurity atoms, there is a pronounced contribution of the "impurity" SLR mechanism, which involves spin diffusion. In this case, the SLR acceleration is caused by the enhanced spin-lattice interaction near the paramagnetic centers due to dipole magnetic and quadrupole electric hyperfine coupling. The use of NMR allows studying separately these mechanisms of SLR and obtaining information about properties of defects, which exist in real crystals. It was previously shown that point paramagnetic centers and spin diffusion are involved in the continuous saturation of gallium spin systems in semi-insulator GaAs single crystals. This made it possible to develop a technique for separating contributions to gallium SLR using the additional resonance continuous fields applied during observation of the nuclear magnetization recovery. Recently, it was proposed to use a more accurate and sensitive technique for evaluating the slow component of nuclear magnetization restoration at positive spin temperatures under magnetic continuous saturation of the nuclear spin system.