Is that what he thinks it is??
Pumps stop for various reasons.
Can be frustrating to find where the fault is, Check the pump relay - identical to the horn / lights etc so check the horn works and swap the relay see if the horn still works or if the pump starts. Cant remember which now and its too dark to check

Wirig loom from ignition switch can fray if its bound too tightly to the headstock, most of us have cut the cable ties to reduce the likleyhood of failure.
Wiggle the handle bars lock to lock with the ignition on and see if the pump comes on.
Check the connector block rear RHS tank that you disconnect to remove the tank.
The female connectors can splay leading to pump stopping, close them all slightly using a slim flat screwdriver blade, reconnect and test for pump sound.
Then I'd check the side stand switch as this is prone to getting filled with crud or the micro switch which activates when the stand is retracted.
Oh and go through all the fuses again checking continuity.
Then Id take the tank off and take the pump out.
Dont spend a fortune @ 200.00 nicker for a new BMW one, there is a much cheaper identical automotive replacement which PEKKA (thanks Pekka me old mate) found and Ive used these last 3 years with no issues. (@ £75.00 if i remember correctly)
All the above has been discussed at times so do a search.
It's not too bad to sort yourself as I found.
