The rear air shocks were shot so I put on some new Monroe'*. How do I tell if the compressor is working and if it is not what is the best trouble shoot method? Cannot hear it running. Tomorrow I will go sit on the bumper to see if I can hear it running. I can usually hear it run I my other Bonneville

You installed new Monroe air shocks, I assume. You should be able to hear the compressor running if it is working.
Check your owners manual under fuses and check the compressor fuse, see if that is in working condition.

I believe the key also has to be on for the compressor to activate.

I believe the compressor is behind the right rear wheel, and should activate within a minute of being sat on. In '93, the FSM directs 300lbs of ballast in to the trunk, but very few people are small enough to sit on the open trunk lip and not trip the ELC to re-level the car. This way you can not only hear the compressor, but you can also feel the rear pump up too.

I'm 430lbs, and can make it work pretty hard if I wanted to