There are wires at the base of the shifter, back up? .....The previous owner made a GT with air. Possibly removing the BU lights in place of GT valance and console removed for aircon unit?
That depression / flat spot behind the shifter where the wires go through is where they drill for the backup light wires. Should be a conical rubber grommet they go through, and looks like it's there. They should go to the shifter "base" below the tunnel where it mounts on the transmission. There you should find a switch that looks like below. That's your backup light switch. Even if it's not there that flat spot is where the 65 wiring manual shows those go through, and think I remember reading that somewhere too. So yes, guessing the P.O. switched out the rear valance.
Just fyi, my Oct 64 SJ Fastback is a 4 speed car without backup lights, and that flat spot is not drilled out & no wiring.
Also, the console can still be used with air, it's just shortened and a chrome cap placed over the end to allow for the under dash A/C unit.