Today I tackled the problem with the rusted rear numberplate lights. The plate that holds them tight to the underside of the bumper had completely rusted away at one side.
I had considered getting some sort of new plate and screwing it all together, but I figured out that if I used the original 2 plastic mounting holes that were now unused because of the rust, I could cable-tie the remaining metal to the bumper.
It's not very beautiful, and certainly temporary at best, but it's definitely a lot better than it was!
When I had the boot open for access I noticed that the light in the boot wasn't working at all. After inspecting the bulb I saw that it wasn't the problem, so I turned to the switch. It seems that corrosion had stopped the switch from closing properly. So I pulled the switch out, and gave the contacts a good clean. All working again!