Re: P0410 secondary air injection
The pump runs a bit when the car is warming up, again, to introduce more O2 in the exhaust so as to heat up the cats faster and keep emissions down.
So you SHOULD hear it. But it might not be running enough or fast enough to make the PTCM happy... In any event, it is no big deal if you have no emissions check coming up.
You can google that code and read about it yourself - it is also mentioned in the emissions section of the service manual.