The vac pump in the boot/trunk is for the pneumatic door locks. Hold over from the 123/first generation 126 era locks that operated from engine derived vacuum.

If you lock or unlock the doors you should hear it whining for a few seconds.

This is the same system used on the W124 and it can be retrofitted with a keyless remote.

__________________
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