Reverse switch problem

Me again.

Reverse lights don’t work. Checked the bulbs and the fuse by the drivers pedal, all seem fine.

So I assume it’s the reverse switch. I’ve bought a spare and tried to swap it today. What a pain that is! I failed.

So I have two questions:

1. Is this possible without dropping the gearbox?

2. I wanted to test it was definitely the switch before I went crazy getting it out, so unplugged the old one and plugged the new one in, put car in reverse and switched on ignition and then pressed the end of the switch in but it still didn’t turn the lights on. Does the switch work this way? That you can push the plunger end in and it should turn on?