Happiness is a new battery. Bought the old one in spring of 2004. Load test confirmed its demise. Can't complain.
New battery came with a tiny plastic elbow and plug to connect it to the battery vent hose. Never seen one of those in a Mini.

Okaaaay... here's what I found:

 - Light switch is good.
 - No light relay found.
 - Loom appears generally unmolested.
 - All parking, tail, license plate and instrument lights come on with the switch in the first position.
Behind grill and slam panel, near horn and centre support:
 - RH front parking light (in the headlight) is fed by a Red/Green from main loom. Factory splice appears OK and able to receive a second output wire to a lamp, though not used.
 - LH front Parking light is fed separately by a Red/Black wire coming from cowl area behind carb. (This single wire is in its own loose vinyl tube shield and appears to be a later addition.) There it is spliced into another Red/Black that is fed from an in-line fuse (fuse and holder in good condition), which is fed from the bottom fuse of the 4-fuse box, fused side. The splice seems to be a non-factory one as it is taped (possibly soldered) and does not have factory bullet connectors. The fuse-holder is the whitish nylon type but the end where it connects to the bottom fuse terminal has the last square black original style clip.
 - Also from this splice a much smaller wire, light brown or possibly pale orange (salmon coloured?) that disappears into a smaller section of loom of approximately 10 wires disappearing into the firewall up near the bonnet hinge. presumably this is the portion of loom going to the rear of the car.
 - From the same fused side of the bottom fuse is another Red wire going into the main loom.
 - The bottom fuse in the fuse-box was working until I touched it, whereupon it made a tiny flash and died. when removing it, I found the metal end-cap was not sealed to the glass tube. The replacement fuse is holding OK.

If I pull this Red wire to the loom from the fuse-box, all the parking and instrument light go off.  If I pull the other red wire feeding the in-line fuse, only the right front parking light goes off.

So, it seems that at some time, somebody had a problem with power to the RH front parking lamp and provided a by-pass wire to it, properly routed and protected with its own in-line fuse.  But I don't understand why (or what) it would be spliced into behind the carb.

In the boot I found the ground wire to the right rear light cluster was loose, as well as the boot-lid wires to the license plate lamps were disconnected. I initially missed the ground wire problem as the other lamps in the cluster functioned.

Now to take the battery for a load-test. Its warranty expired about 9 years ago. The trickle charger does not indicate full charge, and the car radio lost its pre-sets, suggesting a big voltage drop.
This all started when the car didn't.

I just had an issue with my lights drove me crazy. I did find a bad glass fuse (not burnt out, just not making a good connection) on the bulkhead box, 3rd one down, this was for the rear tail light. Replacing the switch corrected my problem.

Did you remove the air filter housing and check the glass fuses (if so equipped) behind it?

How would replacing the switch solve it? The switch works for the left side parking lights and all others.

replace the switch

TTT.
Can anybody suggest why both right side parking lights are unpowered? Left side are OK. Please see car details below. (Too darned hot outside for my health today).

No sign of a dim/dip headlight relay... yet. Meanwhile I discovered the two wires for the rear license plate lamp were unplugged - gotta wonder how long it has been like that! Meanwhile, my trickle charger has a bare 120V wire that needs correcting. Are Lucas problems contagious? 

Dan, not sure on German spec Mini's but you may find the relay on the firewall radiator side.
Check behind the carb in the engine bay, later models have in line glass fuse holders there which go bad with with age and are best replaced with a blade fuse block.
The later headlamp wiring exits the engine bay into the fender well half way down the wings.

Yesterday, the Mini decided not to start. While checking out why today, I found that the right hand parking lights were not functioning. Both bulbs, front and rear check out OK with a multi-meter. Left side parking lights work.  Headlights (high & low), turn and brake lights all work.

Specs of the car:
1986 Left Hand drive built for life in Germany. The front parking lights are built into the headlights. Most of the wiring seems to correspond with Haynes' Wiring Diagram 17, except that it has the starter relay with a brown/red wire feeding the starter solenoid, (which is built into the starter) on Wiring Diagram 18. I do not know if it has the dim/dip relay, #72 on Diagram 18.

Questions:
1. Can anybody tell me where the parking light wiring divides to go left and right?
2. Where should I look for a dim/dip headlight relay to see if I have one?