been there done this one!
99% of the time the terminal has corroded off the reverse light switch.
Easiest thing is to spade a new conection on as the wiring only comes with the loom . If your lucky it might have gone inside the switch and you can just replace the switch £9 from main dealer.
To find it look down to the left of the battery tray halfway down the gear box
on the very front of the car.
dont mess with the switches on the back of the box !!!
Easier to lay underneath and look up. you will see if the wires come off
To test either short the 2 wires together or remove the switch and press it in.obviously with the ignition ON
If it is your fuse then loads of other things would be dead which would give it away.