Agree with that. Switch or short circuit. On ours it was the switch jammed "open".
This was caused by the reverse plunger being jammed shut (it pushes a pin against the reverse switch). Previous owner had got around it by simply removing the reverse light bulbs...
The whole switch was knackered as a spade connector had fallen off too, which would have solved the problem in a rather unhelpful way!! £22 from Land Rover...much cheaper from some of the big spares suppliers as I found out the other day :-(
Took the whole gear selector assembly off the car, took it apart, dropped it in a bucket of white spirit for a few hours and coaxed the pluunger back into life with WD40, ignorance and a vice!! Reassembly involved much use of HT grease.
Also replaced a few of the gaskets and springs in the gearshift and reassembled. So far, touch wood, I have selectable reverse, (some) idea of which forward gear I'm selecting and a pair of reverse lights!!
One tip I have is make sure the wires to the reverse light switch are correctly routed. Ours weren't and as a result were pulled really tight - not a good idea.
Malcolm
Hope that helps?