While mixed ionic-electronic conductors with metal-insulator transition (MIT) are promising candidates for designing neuromorphic computing hardware, the fundamentals of resistive switching in these materials are yet to be well understood. This work studies the switching mechanism of the three-terminal nonvolatile redox transistor (NVRT) containing the LiCoO2 (LCO) channel layer with tunable preferred crystallographic orientation. We used atomic force microscope nanotomography to reconstruct the 3D conductance map of NVRTs, that reveals the applied gate electric-field induces the MIT via reversible phase separation in the LCO channel layer, with the nonequilibrium thermodynamics analytical model providing validation to this mechanism. By operating in the post-percolation region, the memory properties can continuously adjust the conductance states of NVRTs. The percolation conductance mechanism via the metallic LCO phase ensures the exceptional linearity and reproducibility of conductance modulation, whereas the field-, rather than current-, induced transition results in the low energy consumption replicating key features of the living neural cells.