Gentlemen, help is requested please.

The bike: K100LT, 1990, vin number 0179060, FOUR (4) pin Fuel Injection relay (rare but not unheard of).

What's wrong? Fuel injection relay problem and non functioning fuel pump.

The engine cranks over on the starter. No noise from the fuel pump turning. I know it's operative because I've taken it out and tested it very briefly with a battery. I am following Crazy Frog's famed fault finding post.

Neutral light is good, as is the clutch switch, as is the FOUR pin FI relay (12v across pins 85 and 86 elicits a healthy click), ignition switch is healthy, kill switch is healthy (disassembled and cleaned). Fuses are good.

There used to be 12v at the 4 pin petrol tank plug. Not any more.

I've swapped out the ICU for a known good one.

The big problem appears to be no power to pin 86 or 85 of the FI relay .

The wire to pin 86 of the FI relay is yellow/brown. It appears to connect to pin 7 of the female lead to the ICU. There is no continuity between pin 86 and female pin 7.

I don't want to rig up a new wire between female pin 7 of the ICU and pin 86 of the FI relay. 

I'm not afraid to check the HES having recently replaced the same on my R1100RS.

Any thoughts on the malaise of the K100LT will be appreciated.

If there is no continuity on the wire from Ignition Control Unit pin #7 to the FI relay, it would seem that there is a break in the wire.

No, non continuity.

I know this points to it being broken.

I can't see how, being as it is in such a thick and well wrapped loom. 

I am just casting about for other options before accepting that I may have to jury-rig a bodge to connect the two.

Jump a wire from the ICU to the relay maybe?  If it works then you know that it is the wire in the loom.  Depending on your OCD level you could simply abandon the original or, if your personal OCD level is way on the other end. open up the loom and change out the wire for the same colour, guage, etc. 

Under these circumstances, loom reiki might be an option. 

Mystery solved.
I was under the impression that the FI relay was front left in the under-tank relay box. Hence, this is the relay that I was testing when following the fault finding flowchart.
On my bike the FI relay is front right in the relay box (perhaps relocated by a previous owner). 
Once I identified the correct relay, the fault finding flowchart started to make sense and I have now managed to fix the problem.

How did you repair it, Geoff?

It was simply a defective fuel pump/fuel sender connector to the main wiring loom. Once this was made to properly connect, the fuel pump began to work again.