I have a Nighthawk too, and it is a good product compared to other CO detector. My wife insisted on it when we got a gas water heater and furnace about 5 years ago. It has never measured anything but zero except when it when bonkers when the power went off for a while and the battery ran down. It is probably the most useless too in my house. Way, way down the line from a blow torch which I haven't used in 25 years.
Sorry, this isn't helping. If you really want to know what is happening you will have to look at and in the burner when it is off and if you see no cause of the smell, you will need to look at it when the burner is on.