It's been a while and hopefully, I'll find some advice again.

My '85 K100 starts and runs for 6 or 7 seconds and stops. The fuel pump stops about 1 second later. The engine will not start if I crack the throttle or the "choke".

I now this sounds much easier than most anomalies.

Have you replaced the fuel filter since you wrote about the Brick in 2015?

I think so, BUT, will install an new one to eliminate that as a potential cause.
Thanks

You could just remove it to see if you can blow through it without your cheeks and eyes bulging.

Is there any fuel leaking from the connections in the tank?  A leaky connection will starve the engine for fuel.  Once the engine stops, the fuel pump is shut down a second or so later.

A kinked or collapsed fuel hose where it connects to the tank can cause problems. Hot climates don't help as does incorrect specification hose. The OEM hose has a bend built into it where it goes into the tank, non OEM is straight and can be used but needs to be routed so as to eliminate the possibility of kinking. Alternatively you can fit the correct size Unicoil with an extra hose clip below the Unicoil to help keep it in place.
Regards Martin.

Next time you try to start it, keep your finger on the start button. 

If this keeps it running, then your fuel system is running ok, its getting fuel, its getting spark.
What its not getting is the signal from the Hall Sensors to the fuel pump/fuel pump relay. But if its firing with your finger on the start button your Hall sensors are giving signal to the ignition system so its reaasonalbe to assume its not a HES problem.

Check your injection control unit under the seat, the big plug connector and make sure all the pins are clean. It gets power from 2 pins, not one. One is from the start button, the other is from the HES. If no joy then you need to do the same with the Ignition control unit under the headstock.

Thanks for everyone's thoughts.
Although I think my fuel filter is ok and the pump is more or less ok (since it delivered at least some fuel for some time), and all hose connections in and out of the tank were tight, I have decided to change out the pump including the rubber vibration sleeve (the pump was a Mazda unit and there's no vibration cushion).
When the pump set is delivered, I will install all the bits and see what happens and report back.
Thanks again
Klaus