Most reversing switches are either on the box that the gearstick goes into (accessible from under the car) or on the gearbox itself. Usually, the switch is a simple momentary contact one, cheap and easy to replace. Before you change it, you can test the circuit - switch on the ignition (so the lights come on, but dont start it!) then short the connector attached to the switch (use a suitable bit of wire/small pliers/tweezers, etc) and getting an assistant to check if the lights come on. Be very careful if you are under the car - use ramps or proper axle stands - be safe!
JamJam, December 2004