This is resolved after replacing the Thermal Fuse and Ignitor. Pretty sure the old Ignitor was still functional (the new one failed continuity check as well, resistance stabilized around 80 ohms) but I replaced it anyway since I had the new part. Also replaced the light bulb - didn't even realize there was a bulb behind that plastic lump until I had everything stripped down.
I took your advice to clean out the lint trap / vent also. So much debris in there. While I was at it, I replaced the flexible foil hose with a rigid aluminum one for extra protection against the possibility of something falling on it and making a hole that could vent CO into the basement.
Hopefully this will all last a good long while. Thanks again, Dan!