The Deville, depending on emissions package level, came with 0, 1 or 2 AIR pumps. Look on the passenger side strut tower - there is a bracket bolted to the side. It will have 0, 1 or 2 gray relays with blue connectors depending ...............
When you start the engine on a cool morning, window open, do you hear a very low level vacuum-cleaner-like whine inside the driver's fenderwell ? That pump(s) may run for a short period at cold start in order to send fresh air to the exhaust manifolds (oxygen) in order to quickly light off the cat.
but ........... never heard of a AIR pump disable feature.
The only other "air pump relay" would be for the rear automatic level control compressor.