On my 84 500SEL the tach signal comes from the ignition module at the left front of the engine compartment. It is called the TD signal. If the fuel pump relay doesn't see this signal, the car wont run.
I don't know but I believe the Generation 2 gas cars are the same. Also, on the Gen 2 gas cars, the A/C won't work if it doesn't see the TD signal.
Sorry I can't be more specific.

Paul

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84 500 SEL (307,xxx miles)