Outer Limits 4x4 Board

we have checked the bulbs and they are fine
we pulled the switch out of the gearbox and it is fine and working
we have traced the wiring as best we could and found nothing wrong visually
what could be the problem for them not working

In a simple form, reverse light circuits have 12V at the globe, and the switch in the gearbox connects the circuit to earth.

So, do you have 12V at the globes?
Is your gearbox earthed?

I can't imagine that the gearbox isn't earthed - if it's not, I would expect your alternator wouldn't work either, and probably not your starter motor.

You say you have checked the switch how? A simple test for the switch is to bridged the plug out with a piece of wire. revrse lights work then switch is faulty. There is probably a relay for the revese lights and they will switch a power as most tail lights have a common earth. If no relay then power through the switch. One other test is to find the plug that connects the rear lights to to the main harness as sometimes it can be dirty connections.