The testing of the frequency valve circuit is OK, but not necessary. I told you that the engine doesn't need the frequency valve to work.
I'm going yto make a stab at the problem. I say it is a problem either at the C105 connector from the starter or the other end of the black wire going to the upper starter bolt. I am presuming that your total load becomes greater than the circuit can handle. Do you have the ETM 1980. Look on power distribution. The terminal C105 which gathers all the wires from the alternator and starter.
My first test would be to disconnect the load of the frequency valve, the warm-up regulator and the lambda controller. See if the circuit will support the fuel pump alone without opening. The C105 connection is in the front of the LH wheel well. It is a row of four phillips screws bundling the groups of wires attached.
To test this theory properly, one should verify that the battery voltage on this 30 circuit stays stable when the problem exists. Thsi is my theory of what it happening. It can be tested with a volt meter. If I were doing it I would also measure the current in this circuit to see if there is too great a load. My theory hinges on eiither too great a load or too weak a circuit. By pulling down the C105 connection you will drop voltage to ignition and most everything else. The wire dropping vertically supplies the ignition eventually and most everything that isn't going out one of the horizontal outputs from C105 (in the diagram).
Bosch Master, ASE Master, L1
33 years MB technician