Guys,

On my Recent trip out , I was told my Tail light was out.
Replaced it, Still no Joy.
Noticed front parking light also not working.
Both bulbs are Fine. 
Warning Light Didnt come on to tell me ( guess because both bulbs are fine).
Brake Light works.. 
The bike is spotless, original.  
I am Thinking the bulb monitoring unit?
Would anyone know where I could get my hands on one, even just to test..
BMW K1100RS. 1996...

The one thing that could kill a K bike.. the Tail light ..

Reg.

I suspect you're probably right, Reg. The BMU is the only common point for those two parts of the wiring loom, although it doesn't actually monitor the pilot light. Any BMU should do.

Check at fuse three.

Check if the parking lights work with the key in the park position. In this case the power to the  ignition switch is through a different circuit.

Edit: just noticed this is a K1100, maybe not very relevant, I had a K100 in mind.

After much messing about, bypassing the bcu , I decovered just by chance , it's the ignition barrel.. Good clean out , and all is well. Hint ..don't put wd40 or any other oil down the barrel, just use electrical contact cleaner ...Pure luck I spotted it..

Ah. You insulated the slate (grey) wire from the slate/blue wire which is the parking (sidelight) circuit. Just commenting for anyone else that happens to pass this way with a similar problem.

I realise now I didn't say what I was thinking, I only inferred it.

Since the front parking light was also off, therefore the problem was upstream of the BMU. So the first junction both lights have in common is the lights fuse, the next is the ignition switch. Therefore if the lights worked with the key in the park position, the fuse would be good and the ignition switch would be suspect.

But I'm looking at a 1993 K1100RS wiring diagram now, not sure if it's the same as with later models.