The pump should run in both the, "ON" and, "START" positions as you say. So, you are on the mark as I too think the starter switch is worn somehow, but it is odd that the rest of the circuit works and not the pump. The relay will either work or not as long as it is getting power.
So, I believe something has gone wrong with the Immobilizer unit which is part of the anti-theft system. The starter signal actuates it, I beleive it is in diagram 3of3 where you will see starter signal and Immobilizer unit interface. Then again in the Sart Circuit diagram you can see that the starter signal goes into the Immobilizer in hte, "Start" position before going anywhere else. The fuel pump pis controlled by a compuer control unit so it is possible that it gets primed and does not run in the, "Sart" position, see wiring diagram for fuel pump control unit, and that will have to be assumed since I don't have circuit level board breakdown descriptions of the immobilizer or fuel pump control module.
I believe you need to have the Immobilizer unit re-coded and I have seen this happen before. There are many reasons why it can happen and it is all in the control units so again I can't explain to you a fault at the circuit board level. I can only tell you the re-code procedure, attached, and then tell you to have the trouble codes pulled when re-coded to see if something comes up.
I have seen this happen and the re-code has taken care of it and I have seen cases where control units get replaced. This is just the next step you have to take.
I don't think you have to go to a BMW dealer for re-code. Just ask shop if they have MoDec, you will see the name of the coder I am talking about so if I am mis-spelling it. Forgive, and if they have one it can be done as long as they know the procedure. It should not cost a lot and then you can have the codes pulled at the same time. The cost is in getting it to a shop, I wish there were a quick fix I could giove you.
I provided all pertinant wiring diagrams and the re-code procedure.
Images (click to enlarge)
Tuesday, August 28th, 2012 AT 12:39 PM