So the "key on" prime is just a time controlled action? It isn't a "run to pressure value" sequence?
I did not see a pressure sensor when I had mine apart, but I didn't know what might be integral to the pump.
The short prime sequence (after ignition ON) is just timed by ECU (BOSH Motronic) and is NOT based on reaching a certain pressure to stop prime action. The whole system design really does not care if you prime 3 sec or 10 seconds as the surplus goes back into the tank anyway (by design).
In order to spare fuel-pump from overworking for no valid reasons, I have to assume they did some engineering test to get an acceptable prime time that would satisfy overnight cold start. The overnight cold start is where the prime duration is the most important as tests (using pressure gauge inline) shows that there is a slight loss of pressure over several hour period (mainly caused by leaking injectors).
In fact, you could easily prove yourself that the system is closed internally (to maintain pressure when stopped) and stays "somewhat" primed when engine is stopped for a short time:
(1) with engine already warm and fairing off, disconnect fuel pump connector
(2) turn ignition ON, wait 8 seconds (just for ABS init and self test to finish)
(3) plug back the fuel pump connector (there should be NO priming noise)
(4) start engine as usual
If you did the same with long hours overnight stop, it might not start so well as you will have some internal pressure leak. It will still start but will require a few engine rotation (hall effect sensor is the trigger to fuel pump signal).
The whole EFI system of the K1200 "brick-engine" (like the K100 and K75) is NOT aware you have by-passed the prime sequence with above steps - there is no pressure sensor anywhere, just a "dumb / simple" fuel pressure regulator. As stated in earlier post, the newer BMW engine models EFI systems are very different compare to this.