I had a good long look at the electrical diagram and it doesn't show a separate switch for the reverse. It just shows the pod (#51) and the speedo gauge as a single unit (#52) and there is only one wire going from the pod to the ECU (L/Y) so I assume that the single wire works similar to a car ECU and uses a data bus or something similar to do the speedometer and the reverse signal. When you push the reverse button, it sends a data signal to the ECU instead of a regular 12V signal.
If the fuses, relays and servo check out and all connections are clean and corrosion free, it may be possible that the switch in the speedo pod is dirty or corroded. It looks like it is likely just a carbon type contact, similar to TV remote controls. I could see that happening on the Phazers without windshields as it would be exposed to a lot to snow and road salt from open trailering. The bracket on our '09 was corroded from being exposed without a windshield by the previous owner but the one on my '07 VMP is pristine.
Before opening up your pod, I would find someone with a known working pod and replace it temporarily to see if that is the cause. If it works, then your switch is defective. You could attempt to take it apart and clean the switch or replace the pod.
EDIT: Just noticed another wire going to the ECU (B/R). Then what I said is incorrect. It is likely one of the two wires that sends the reverse signal but don't know which one. I still suggest borrowing a good pod to try out