Air compressor runs with engine off?

[bcc]

Car is sitting in garage, engine is not running and key is not in car. At random times, the air compressor will run for 30 - 40 seconds and raise car. Is this normal or should the air compressor only run when engine is running?

 

[joegr]

I don't know specifically about the Equus, but most cars with air suspensions will allow the compressor to run with the engine off. Usually, there is some timeout, such that after an hour or two, it wouldn't be allowed to run again.
The fact that yours is coming on without any one pushing on the car or adding something to the car, indicates that one or more of your air-springs is leaking. You want to fix this sooner rather than later because it will wear the compressor out and then you will have to replace that along with the air-spring(s).