It's been doing this for a few years now... I've just ignored it because I thought it was a coolant leaking slightly into one of the cylinders, and that was messing up the spark pug which caused the sputtering. That's why I had the gaskets done last year... plus it was losing coolant and occasionally smoking from the coolant. But the sputtering didn't go away after the head gasket. So, if it was a weak pump, it surely would've died by now. As far as a bad check valve, I guess I could check that in the morning by turning the key off an on to make sure the pump primed the line.
If there is something wrong with the TPS, how would I troubleshoot that? Where is it and what should do?