A while back the reversing lights were not coming on. G checked the bulbs, they were OK, so was the switch in the gearbox.
When in reverse with the ignition on there was no live at the bulb. After tracing the wiring it turned out to be oxidised contacts in a 3 way connector under the bonnet (see pics), about the last place you would expect to find it.
The same connector is used by the start inhibit circuit. Any problems with start inhibition should also be checked here first.