P0410 code

I have a 2000 chevy S/10 which I replaced the AIR pump about 3 months ago because of the dreaded P0410 code.Found it full of water and not operable so out with it and new one in.Code came back so I changed relay,code was gone and is back again.My question is as I drive even after 10 mins. after starting vehicle the pump will cycle on maybe three times for a short 5 sec. burst and shut off and it is random not every time.I wonder to you the knowledgeable car talk community if this would point you in a particular direction(ex.blocked hose,bad check valves,solenoid switch).I had the trans rebuilt 05/10 and have a 2 yr. warranty which is acting up (hard shifts,also slight jerking at 40 mph like it’s seeking probably a valve issue)and the shop owner (rhymes with waamco)has told me he cannot do anything for the trans till the codes are cleared.Thank You car talk for this place.

I had this on my Saturn and could not find anything wrong with the AIR pump, check valves or tubes. Thanks to another poster’s suggestion, I checked the molded in tube in the exhaust manifold.

There’s not much you can do but to pull the tube from the check valve out of the exhaust manifold, then use carb cleaner. Stick the red tube that comes with the carb cleaner into the hole in the manifold and spray until you finally get it to spray into the manifold instead of back on you. Wear protection when you do this, especially eye protection.