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I've got the old P0410 code popping along with issues with the vents switching between feet and dash. After reading through here, I dug out the battery and battery tray to have a look around, and there are no signs of battery acid leakage.
I was curious if the sensors getting clogged over on the other side of the engine can also cause this. I didn't get real in depth, but it seems that the vacuum line from rear of the intake manifold down to the passenger side access panel is OK, so I am trying to hunt down other reasons that might be triggering the code and HVAC vent issue.
If you have the AIR system installed and operating I’d look for the AIR pump to turn on during a cold start of the engine...just put your ear up the left front tire...you should be able to hear the pump run...if not there is a AIR fuse #50 and an AIR pump relay #33 to check initially !!...if the pump is running and you have a scan tool you can check to see if the solenoid and shutoff valve are operating by watching your upstream O2 sensors go lean or your short term fuel trims go positive !!
I turned mine on with the scan tool and it’s a lot louder if you open the hood and listen at the left hinge area...if you suspect the relay you can swap the AIR relay with the horn relay just to check...the engine has to be in “closed loop” for the PCM to check it so it might take a minute or two to hear it...and now that I’m thinking about it your HVAC and P0410 issues are inter related...VACUUM hoses on both (AIR vacuum controlled solenoid is like it says...vacuum controlled) !!