That nozzle in the trunk is actually for using the onboard air pump as an inflator to air up things like tires, balls, etc. There should be no air coming out of it or pressure building from it unless switched on using the nearby trunk switch.
The air system is designed to level off the rear end as weight is added loading the car down. Ideally, the car should set level with no extra weight in the rear. Usually the Factory service manual advises to confirm correct operation by throwing 300lbs of ballast in the trunk (causing a visibly low rear end) and then turning on the key. The car should fire the compressor within 30 seconds, and level off soon after that. You can also turn the key on, and with the trunk open, sit on the trunk lip, and it should get to work soon after sitting.
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~Randall~
1993 Buick Park Avenue - 197k - Some odds and ends done - Simply won't die
1994 Buick Regal - 78k - Bone stock - Always ready for a good kicking
1990 Oldsmobile 88 - Gone to a better place