So u think the MB engineers smoked too much when designed the ground strap there in the first place?
Can try jamming your brakes see if ABS will kick in. Mines did work few mths ago when the ground is all glaced with frost.
Isn't the control unit a big steel box sitting on the driver side of inner fender , which has 2 or 3 brake lines go in and 4 B lines exit.

If I am correct thats the unit do the pumping / pulsating action for the ABS.

It should have a four motor pumps inside too. So if there's motor there will need grounding.
Your brake rotor has magnetic star wheel monitor the speed of the rotor when it stopped it should start the pulse.

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