My pump will run with my foot on or off the brake. I called around and spoke with a few shop foremen to get their take on the issue. From what I understand, the later model (94-95) E-Class perform a self test that actually activates the pump where as the older 124s' self test does not. Either way, I replaced the rubber mounts from the pump to the car which helped to damper the vibration from the pump running which helped a little bit.

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1995 E420
1998 SL500 Sport
2009 E350 Sport
1995 S500 Coupe
1992 500 SEL