Possible that the AIR pump is “making the car run like crap”, if it's simply not turning off when the PCM enters closed loop. Would be a very unusual situation. The only code in OBD-1 for the AIR system is DTC 29 for the pump relay control system. That code sets if the relay is energized when the pump is supposed to be off, or if there is an open circuit when the AIR pump is supposed to be running. Either case is typically a relatively simple electrical problem.

More typical problem is the fuse for the AIR pump is blown, and pump isn’t running when it is supposed to. The AIR pump only runs for about 3 minutes after engine startup, to burn the excessively rich cold start A/F ratio exhaust, and thereby heat up the O2 sensors and the cat. After ~3 minutes, it shuts off and does not turn on again until the next engine start. The pump not running during cold start would not materially affect the way the engine runs. The pump running after the PCM switches to closed loop would totally screw up the A/F ratio and cause the engine to run pig rich.

There is no need to be “programmed out” in OBD-1. Simply unplug the harness connector at the pump, and make sure there is a good fuse in the circuit = no code.

Probably be a good idea to figure out what is causing the problem first.

As noted, DTC 29 could be due to a wiring problem causing the pump to run all the time. If that problem was caused by a faulty relay, or a short in the wiring to the relay, even after you do the “delete”, your going to have an SES light. If the problem is a blown fuse causing an open circuit at the relay, replacing the fuse after you unhook the pump will not result in an SES light.

I'd say that 95% of the time DTC 29 is due to a blown fuse. But your statement about the problem causing the engine to run badly may indicate a different problem. That's why I explained how the system works, before telling you how to delete the pump. Have you verified that the SES light is on because of that DTC?