All that pump does is inject air in the exhaust to heat the cats faster. No big deal, but you wo'nt pass an emissions test.

Usually, the problem is broken solder joints or a bad relay on the Relay Control Module. I'd pull the module and get any odd-looking joints re soldered at a radio shop.
There is a "How to" here on it - search "RCB" or "how to relay control board resolder".

If that does not do it, go from there: the relay itself, connections to the air pump or air pump itself.