Tach signal is derived from the EDS controller that lives behind the battery.

If you are running crappy with no tach then it clears up and you have good tach I would suspect the OVP relay as well. It's back there with the EDS controller.

First I would check the big plug on the EDS and be sure it is plugged in securely and not corroded.

Aux pump, try the yard first if you want to go cheap, new ones are $$. Bring a 12 V drill battery and a couple clip leads with you to test it before you pull it.

Alarm controller under passenger feet, pull back carpet and remove plate. Alarm controller is the black box on the floor. Leave the red plug alone, that is the maintenance plug for your airbag/seat belt pyro tensioners.

__________________
The OM 642/722.9 powered family
Still going strong
2014 ML350 Bluetec (wife's DD)
2013 E350 Bluetec (my DD)

both my kids cars went to junkyard in 2023
2008 ML320 CDI (Older son’s DD) fatal transmission failure, water soaked/fried rear SAM, numerous other issues, just too far gone to save (165k miles)
2008 E320 Bluetec (Younger son's DD) injector failed open and diluted oil with diesel, spun main bearings (240k miles)

1998 E300DT sold to TimFreeh
1987 300TD sold to vstech