Rear n/s fog light failure.

It sounds like your wiring in the boot lid is broken. There is a rubber tube where the wiring loom leaves the boot lid and enters the fender.
Here, the wires got bend every time you open and close the lid and after so many years the PVC isolation of the wires get brittle.
Then it's only a matter of time before the wires break as well.
You have to replace this portion of the broken wire.
Do not try to solder the two broken ends together as this would only last a short time.
Inserting a new (preferably silicon-insulated) wire piece solves the problem for a long time.

Cheers
Steve

Rebuild it with this repair kit from Thomas Engl.
Works perfect. I did it 4 months ago.

http://engl-production.de/heckklappenkabelsatz.html

try this.

turn on fog light. if you have no light, try to open the boot lid. if the light comes on you have a wiring issue.
What happens is that when you open the lid you get ground to the lights through the boot light switch.
The ground wire is typically the first that breaks, and its the thickest one.

I had to do a repair on my car several years ago, I noticed the the inner tail lamp was not working, fiddled with it and it started working, closed the lid and the light went out. cut open the wire protectors and the ground wire was broken, and several of the other wires were damaged but not yet broken.

Yes, blooming nuisance! Here's how I did my one:

http://www.meeknet.co.uk/e31/B…t_Hinge_Wiring_Repair.htm

Some Suggestions based on my experiences:
- if not yet damaged, don't cut the outer black tube. If you grease the outside of it, the rubber plugs slide up or down easily. Then you can pull it up to see the damage. It's a bit of a hassle to get the rubber back on this tube after the repair is finished but with grease and some wood sticks it was no Problem for me. This black tube (I don't know the proper name) is not available from BMW and have to be sourced elsewhere if damaged.

- cut the wires far away from this area (underneath the fender rubber plug and above the boot lid rubber plug). This way the rigid soldering point will stay out of the area which get bend all the time. It's the rigidity of the original PVC insulation which makes the wire break. The copper wire alone would actually not break as the bending radius is large.

- use the old wires to pull in the new ones trough the rubber plugs. After you cut the old wires further down, solder the new ones to the old and pull the wires trough the rubber plugs. Saves lot of hassle.

- if possible, use silicon insulated wires. PVC plastic has softeners which disappear trough the years and therefore it hardens and breaks.

Cheers
Steve