This reminds me of the old Ford Escort issue with corroded earths on their light clusters. Basically everything would work fine with the lights off, indicators would work ok, and cars would even pass MOT's because each light worked in isolation. But if you turned the lights on, or put the brakes on, AND turned the indicators on, the whole cluster would dim with the indicator flashes!!! I did find it quite funny to see some of the earlier Mondeos with the same
problem, you'd have thought they would have fixed it by then!
Anyway, back on subject. Basically what I'm saying is check your earths. With bulbs being in a plastic light cluster, the earth is a piece of wire that has to end up attached to the chassis in some way, if its making a bad contact then you've got voltages going all over the place instead of down to earth. This includes the tailgate light, so don't exclude it from the investigation.
If you have a multimeter with a resistance setting, put one lead on a clean earth and the other on the side of the bulb connector (remove the bulb). You should be reading virtually zero resistance.