The easiest way to see if the automatic air suspension is working is with another person. Start the Spder, put it in gear, and lower the suspension all the way. You may feel it move and hear the solenoid valve release, but have someone measure to the rear fender from the floor or ground. Next, raise the suspension all the way. The compressor should run and the Spyder should rise a few inches. Have it measured to the fender again. If the measurements are a few inches different, the ACS is working.
To test the shock itself, push down hard on the rear trunk or seat, then let go. The Spyder should rise quickly, then settle down. If it bounces a few times, the rear shock is shot, and needs to be replaced. Same scenario if you get a pogo-stick effect when you pass over a sharp bump. You will get a big bounce, but you shouldn't get a series of big bounces from a single bump.