Engine won't shut off instantly/'82 300SD

It looks like I might have a vacuum leak. After turning off the engine via the steering column the engine still runs for about 2 seconds. If I press on the diesel pedal the engine will actually speed up a little then shut off. I would would like to know: Is the system under positive pressure or negative pressure? How do you test the fuel pump stop diaphragm to see if it holds pressure? Also the door locks still work but the brake booster isn't as effective recently as I have been having these problems. Wouldn't that mean that my air pump is fine and that the leak is probably the diaphragm at the pump or in the line next to it? Also what activates this diaphragm? Is air pressure constantly supplied to it and is it activated mechanically through a cable or is there some sort of relay on it which connects it to the lock cylinder on the steering column?

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