Hi, my name is Marty. No the seat up down movement is electrically controlled by a motor. It is not controlled by the vacuum pump in the trunk.
You have motors for each function, fore and aft, up and down. It sounds like the up/down motor is faulty or the switch is faulty.
A voltage test needs to be performed at the motor to see if it is getting power and ground when the seat switch is activated. The seat switch can be tested with the Mercedes Star Diagnosis tester. The tester can view the actual values of the switch when it is activated to see if it is sending an up/down request to the seat module when activated.
That can be difficult to track down unless you can catch the problem while it is acting up with the Mercedes tester connected. It's a similar type of test with the Star Diagnosis tester. The actual values of the ignition switch need to be checked to see if the switch is sending a starter request to the engine control module. Additionally, the signals from the transmission control module need checking to see if the module is reporting that the car is in park. You may have an intermittent fault in the ignition switch or there could be a fault in the gear selector module or transmission control module.
The engine control module sends the start authorization signal to the SAM to activate the starter.
Let me know if you need anything else. If you would take a moment to rate my service before you exit the chat I would appreciate it.