My understanding is the pump runs on startup for a short period for initial fuel/air mixture adjustment until CATS attain temperature and the ECU takes over. My experience was the P410 code was generated because although the pump ran correctly at startup, the dirty/corroded contacts on the RCM relay caused the relay to intermittently chatter (make/break) while driving. It took awhile but I finally made this observation when came to a stop at a light one day and I heared the high-pitched whine coming from the the air pump again uneccessarily. Fortunately, replacing the RCM solved the issue for me without needing to replace/rebuild the air pump.