I installed just the circuit board in the car and the "headlights on" alarm works so it is definitely something that happens when the circuit board is placed in the box. I don't want to drive-around with just the circuit board installed as the edge of the board was cutting-into a wire bundle above so I'm back at making the board work while it's in the box.
As the Fasten Seatbelt light has always worked and looking at the schematic some more I think GP403 is right that a connection with one of the pins is "going bad" when the board is put in the box, I think it's something to do with Pin_3 for Power(-)
I've found a shop that will repair the board, they said they could also manufacture clones. I am 50/50 of whether to repair or clone (to clone is obviously more expensive) but I have some time as I don't drop-off the board with them until the weekend, PM me if you want a modern clone.
... and to wageslave's point, it appears some Pontiac/Chevrolet cousins are part numbers 10021724 and 10037040 (thank you, oemcats.com) and one of each is on eBay, though the 40 has eight pins (instead of the seven on mine).
I'd rather figure-out what is wrong with what I have as at this point, it's the principle of the thing.