W124 electrical issues - radio, glovebox light

Hi all, was hoping for some help getting an electrical issue on my W124 sorted out....

There's a red light on the centre console that flashes when the ignition circuit isn't live (presumably it's meant to look like a car alarm). This worked as expected until recently when I fitted a radio to the car (I bought it without one installed but the connectors were there). I noticed that the red light would flash faintly when the radio was on.... I then also noticed that it did the same when the glovebox light was on.

I then noticed that opening the glovebox (so that the light came on) would make the radio cut out.... it would come back on when the glovebox was closed. Now the glovebox light isn't working at all.

Any idea what might be causing this? I'm presuming that all these things are related, and that if I can find out what it is I can - hopefully - fix it AND will have learnt something new about how the car electrics work.

BTW I opened the fusebox and cleaned the ends of relevant fuse but it didn't make any difference. I'm going to replace all the fuses anyway as some of the ends look a bit corroded.