We have previously reported that an ABA triblock copolymer with poly(ethylene oxide) as the B block and a thermo-/photoresponsive random copolymer of 4-phenylazophenyl methacrylate (AzoMA) and N-isopropylacrylamide (NIPAm) (P(AzoMA-r-NIPAm)) as the A block exhibited a reversible photoinduced sol-gel transition in a hydrophobic ionic liquid. Such reversible sol-gel transitions can be used to realize photohealable ion gels. This study contributes to a deeper physicochemical understanding of the photoinduced sol-gel transitions observed in the ion gel, showing that the glassy state of P(AzoMA-r-NIPAm) block domains is responsible for the long relaxation times. Importantly, the controlled photoisomerization of azobenzene moieties allows the glass transition temperature of P(AzoMA-r-NIPAm) block domains to be varied by choosing irradiation conditions. The photoinduced sol-gel transition can be understood as an elastic solid viscoelastic liquid or a viscoelastic solid-viscoelastic liquid transition, depending on the dissimilarity in the magnitude of relaxation times under visible and UV light.