You seem to have two issues, one is the closing assist pump, which evidently has been worked on by someone who chipped the port nipples. The isuue is the pump has two functions, one is to shutoff when the diaphram contact is interrupted. The second is a timeout if it runs longer than 10 seconds. see article
V12 Uber Alles, Getting to know your Closing Assist Pump in a W140 Mercedes Benz, an article by Brett Allison
The second is your locking pump your locking pump seems to have a leak in the lines since the doors all share the same source, it is pressure to unlock and vacuum to lock. This pump also provides pressure for the lumbars and vacuum for the HVAC when the engine does not in two seperate reservoirs, and also has a timeout function. If the rear doors function, look for a leak or obstruction in the front door line, and dont forget it also services the fuel door and trunk lock.
There is a tool called the Mighty-Vac which allows you to draw a vacuum and a guage to see if it leaks down
