Not exactly sure about your truck and what was stock, but radios typically have TWO +12v wires; one wired to +12v battery (constant) and one wired to +12v switched (accessory). the constant connection is just for maintaining settings, presets, etc and is a very low draw. the other powers the internal amp and needs to be wired to your accessory (ignition switch position 2) side.
i don't have a 60-series EWD (wiring diagram) but it is probably not far off from my '95. the stock radio gets constant/battery power from the DOME fuse. ACC switched power comes from the CIG fuse. if you don't have any factory wires left to use, go find the comparable fuses in your truck and you can re-create how toyota did it