It will be the reverse light switch. Mine got worse and worse til I could only get it to work some of the time if I held it.
Its a common problem, and really easy to fix. What happens is that the switch itself fills up with gearbox oil and stops contacting. All you need to fix it is a jack, some brake cleaner and a spanner.
Jack the passenger side, look at the side of the gearbox and figure out which of the two switches is the reverse light switch ( I got a diagram from opposed forces to find mine) undo the connector, unscrew the switch and then with it in your hand operate the switch while you spray the sucker full of brake cleaner til no more comes out.
There will be LOADS in there.
Once you have no more evidence of oil coming out let it dry, and reinstall it.
You now have reverse lights.