Here is a Technicl Service Bulletin from GM concerning this code.
Bulletin No.: 04-06-04-015
Date: March 22, 2004
Check Engine Light On, DTC P0410 Set (Replace AIR Pump, Install New Hose Assembly)
1999-2003 Chevrolet Blazer, S10
1999-2001 GMC Jimmy
1999-2003 GMC Sonoma
1999-2001 Oldsmobile Bravada
with 2.2L or 4.3L Engine (VINs 4, H, 5, W - RPOs LN2, L43, L35)
Some owners may comment on the check engine light being illuminated. Upon investigation, the technician may find a DTC P0410 indicating that there is a concern in the secondary air injection system.
Water may have collected in the AIR pump or the vent solenoid and frozen or corroded the pump.
Replace the AIR pump and install a new inlet hose and solenoid tube assembly using the following procedure:
1. Prep vehicle.
2. Raise vehicle on hoist.
3. Remove shield covering AIR pump.
4. Remove hose and vacuum lines from pump and solenoid.
5. Remove AIR pump inlet hose. Do not re-use.
6. Disconnect electrical connectors from pump and solenoid.
7. Remove pump mounting bolts and pump.
8. Transfer isolators from the old pump to the new pump.
9. Install new AIR pump and bolts to vehicle.
Tighten the bolts to 17 N.m (12.5 lb ft)
10. Route new hose assembly up between engine and fender. It should come up near the area between the battery and the coolant bottle.
11. Connect new inlet hose to pump inlet.
12. Connect old outlet hose to pump outlet.
13. Connect electrical connector to pump.
14. Connect electrical connector for solenoid to connector on the new hose assembly.
15. Connect the hose with the white nipple to the vacuum source hose.
16. Connect the remaining hose to the shut off valve.
17. Install shield covering AIR pump.
18. Lower vehicle.
19. Remove coolant reservoir nut nearest the battery.
20. Route new hose assembly between the battery and the coolant reservoir with the solenoid on top.
21. Install the solenoid bracket onto the coolant reservoir stud and reinstall the nut back into the vehicle.
22. Use a wire tie to keep the new hose assembly away from the engine. On four cylinder engines, tie to the AIR outlet hose. On six cylinder engines, tie to an available hole in the radiator fan shroud.