If it IS the air pump, and it comes on then goes off, then probably not the relay.
When the relay contacts go, one of 2 things happens :
1. the air pump NEVER runs.
2. the air pump runs till it burns up. ( you can usually hear and smell this )

Pull the big orange 40 amp fuse out of the RCM and see if the air pump is really what is running.

Where in Alabama ?