1997 850GLT - Air Pump motor run-on problem

CAR: 1997 850GLT Turbo Wagon -- 65,000 miles.

PROBLEM:

With the engine shut off, the air pump motor keeps clicking on for about 2 seconds twice per minute. I have had to remove the black ground lead coming from the air pump to get it to stop doing this. I am not getting any warning lights as off yet.

QUESTIONS:

1. Will not having the Air Pump connected do any damage to the engine, ie; make it run too lean, etc?
2. What are some likely causes for this problem? Could it be the relay?

Thanks