Have you checked the lamps ?
Reverse sensor switch in the side of the gearbox next to the passenger side drive shaft its green and costs about £30ish
Drain the box job to change
You don't have to drop the box oil just to change the sensor... You just need fast hands and you'll lose about 50ml of box oil. If you jack it up enough on the passenger side you won't lose any.
Health and safety notice: Do not attempt this work shortly after driving the car for hours. Gearbox oil gets very hot and will make you use naughty words if it touches your skin so allow it to cool.
Mick