Hmmm- that's not what I thought.

Very early model D-jet cars had the cold start valve controlled by the computer. Then they switched (for whatever reason) to the different system controlled by thge thermal timer. The circuit is thus:

1) A wire attaches to the starter - and current is supplied when the starter is engaged
2) That wire goes to the thermal timer switch - which breaks the circuit when either the engine is warm or it has been engaged long enough to warm itself electrically
3) From the thermal timer the wire goes to the cold start valve
4) The other terminal on the cold start valve is grounded.

So from my understanding it doesn't have anything to do with the fuel pump or even the computer. It just opens the cold start valve while you are actually cranking when the engine is cold (and you haven't been cranking for too long).

Old D-Jet cars don't have a Hall sensor - they just have trigger contacts in the distributor. But I firmly beleive that the pump pre-run doesn't have anything to do with the position or state of those triggers - I think it is built into the computer to build pressure slightly, and allow the car to start fractionally quicker by having the fuel PSI a bit closer to 28 psi when the engine starts cranking.

Here's a nice link for D-Jet troubleshooting and theory:
http://www.thebenzbin.com/mercedes-d_jetronic_1.html