The 300SDL has an electric pump below the rear seat for the central locking, right? It seems that you'll have disassembly no matter where you start troubleshooting.
Since I don't have a W126 manual, I can try to provide some useful info for the similar system in the W124. The W124 (300D) spec for maximum time to unlock or lock for any actuator is 3 seconds from any point being unlocked (driver's door, passenger's door, trunk). During this testing, the operation of the supply pump should be listened to. If the pump is operating, first, test the system for leaks, second, test the pneumatic function of the actuator. If the pump isn't operating, the electrical portion of the system is tested first, then the electrical operation of the actuators.
Again, for the W124 300D, the spec is > 420 millibar after 3 seconds from unlocking (pressure) or locking (vacuum). There also is a spec for "safety switching time" after the pump is disconnected from the "line" system (off after 25-150 seconds) upon operation of the central locking system.
Hope this helps. It sounds like it could be the pump...but you'll have to find the tests for the SDL to really figure out what it could be (the specs might be similar
). I'm curious to see how close the systems between the W126 and W124 are...