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The A.I.R. , or Air Injection Reaction system, which includes the pump, is an emissions control system which helps reduce Hydrocarbon, Carbon Monoxide and NOX emissions. It causes the catylytic converter to heat up quickly, which helps control the emissions. The pump runs on startup for about 3-4 mins whem the engine's ECM is in the open loop, after this period, the ECM is in closed loop, and the pump is off. Look at a repair manual for details.
About the dual exhaust, I don't think you need it because Ive seen air pump eliminator pulleys for '84-'91 models, which don't have a true dual exhaust. Only '92 and up has true dual exhaust, so you should be ok! Actually, my pump is acting up, and whistling, I can't find an eliminator for my LT1. As far as passing emissions, it seems to be ok, because its only operating for a few minutes after startup. Hope this helps!!!
Forgot to add!! The pump actually pumps air from the air cleaner into the exhaust manifolds through the exhaust, basically. For a real sequence of operation, consult a manual, or do a search...