Memristors, a cornerstone for neuromorphic electronics, respond to the history of electrical stimuli by varying their electrical resistance across a continuum of states. Much effort has been recently devoted to developing an analogous response to optical excitation. Here we realize a novel tunnelling photo-memristor whose behaviour is bimodal: its resistance is determined by the dual electrical-optical history. This is obtained in a device of ultimate simplicity: an interface between a high-temperature superconductor and a transparent semiconductor. The exploited mechanism is a reversible nanoscale redox reaction between both materials, whose oxygen content determines the electron tunnelling rate across their interface. The redox reaction is optically driven via an interplay between electrochemistry, photovoltaic effects and photo-assisted ion migration. Besides their fundamental interest, the unveiled electro-optic memory effects have considerable technological potential. Especially in combination with high-temperature superconductivity which, in addition to facilitating low-dissipation connectivity, brings photo-memristive effects to the realm of superconducting electronics.