Spent another evening poking around inside the Heathkit IG-102 signal generator, this time with schematic in hand and probing around with my DMM to check voltages in various places. I wanted to make sure everything was working ok, and it seems to be. The voltages I was getting were all pretty close (within 10%) of what was printed on the schematic.
I also replaced the original 60s or 70s era power cord with a polarized power cord (harvested from I don’t remember what now). It was a simple replacement and probably not critical but I figured having a new(-ish) cord might make it a little more electrically safe. The hard part was unsoldering the old cord and getting the plastic strain relief thing out of the chassis.
I was able to set my HT to a few frequencies in the 10-30 MHz range and heard tones when I adjusted the signal generator to those frequencies. That seems like a good sign it’s working.