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Ok, are you the one in Oz? I ask because there was no such thing as an F100 in '86 in the US or Canada. And that white thing doesn't look like anything I've seen on these trucks.
So, you are in Oz? Would you, please, put that in your info in the user control panel so we don't have to ask every time?
Your HVAC system appears to be quite different from ours. But, are you sure that is a wire and not a hose? If it were a small vacuum hose it could connect to the white thing. However, I don't know what the white thing is. I see that the top screw slot appears to be elongated for adjustment. Have you pulled it off to see if there is something behind it that moves it?
Does the air temp arm activate the plunger? Perhaps it provides vacuum to a shutoff valve in the water supply to the heater core when the temp is set to its coldest setting. Check the heater hoses for a vacuum-controlled valve.
I would guess it is a cold air valve, or something like that. We don't have them here, but sure wish we did as we have hot water flowing through the heater core at all times, and that makes the Max A/C and Vent positions warmer than they need to be. So, if you find out maybe we can incorporate them?
If you can't find a replacement, can the existing hose barb be repaired?
On other vehicles with similar damage, I'd carefully drill a short way, stopping well short of the internals. Then fit a short piece of brass tube to create a new hose connection. Secure the new brass piece with epoxy on the outside only, and you're good as new. I've done this several times on vacuum parts that were otherwise unobtainable.