Open up your electrical bay cover, and see what's in there along the bottom of the bay. Should be labeled.
Would be nice if you could change it to mechanical relay. Electronic ones aren't as forgiving and will probably be unobtanium down the road.
In normal operation in a stock bus, the heater water shut-off valves are all left open fully all the time. That means you can get dash heat for the defroster, which you sometimes need even in summer, and control the AC temp. There are three water shut off valves, as far as I am aware - the main return valve is down on the passenger side engine rail, after the electric on-off control valve. The main send valve is up above the transmission and you reach it through one of the floor hatches. The driver's heat return valve is up above the rear electrical panel on the driver's side. And of course there is the driver's heat control valve beside the driver's seat.Next - in the summer when they want full cold, the temperature control pot can achieve that by turning the mercury switch heater on fully. If it's full on, the switch is always closed and the electric water valve never opens, so no heat. It's probably set up for a minimum coach temp of around 68 degrees or so, and that is controlled by that voltage divider with the resistors and the potentiometer. The mercury switch is located in one of the cold air return ducts, mid-bus, on the floor. I suspect a lot of converters rip it out and cover up the ducts, at the same time screwing up the factory heat/air. You are unclear if your Tell-tale actually turns off at 82 degrees or not. If it does, that implies the mercury switch is still in the circuit, so you are half way there. If, as I suspect, the black lead is part of the 2250 ohm resistor circuit, that might disable or change the set point of the mercury switch heating circuit, which would remove or change the ability of the circuit to control the temp down below 82 degrees. The whole 82 degree thing is a maximum temp setting not to be exceeded. Finally, my manual on/off water valves are multi-twist deals just like an old fashioned hose faucet - turn maybe three or four full turns to fully open or close. I've tried to use this to control the interior temp, like a variable flow deal, but honestly it doesn't work. On my bus the AC is gone, the factory heat remains, the electric flow control valve is disconnected and I just turn the water on manually when it's cold and control interior heat by turning the fan on and off. Now that you have prompted me to figure this whole deal out I may try to fix it...
Cool, who would have thought that you could get that so easily. Obviously don't forget to install the actual relay in the socket!