The aluminium housing on the back of the gearbox can be reached from under the car, even on cars equipped with overdrive, it's awkward though. Easiest is to use one of those tiny ratchets with a screwdriver bit in them.

The spring switch is available loose, very cheap. Most common problem though is that someone pulled the wires out of the taillight assembly. The relay is always live with the ignition on, ground out the wire going down to the gearbox and the reversing lights should come on, if they don't you have a fault other than the gearbox switch.

Regards

Pete