Gotta love going to look something up, only for the only thread on the part numbers you search to be... your own from 2016, when the only info the people you asked on the forum could find, was stuff from the right manufacturer but that totally doesn't match up with the part you have.
So the context on this is... back in 2016, I snagged a gasolene-burning coolant heater off ebay, with "E34" scrawled on the side of it. It's got a BMW part number of "64.12-8 390 808", and a Webasto part number of 223750. And, crucially... it only has one, 3-pin, electrical connector.
And the only documentation they could dig up, is for the modern style with a bunch of connectors across the top. It's been pretty hopeless trying to find any info on it.
UNTIL NOW
I managed to track down some documentation, and it lines up with what I have. Turns out there's a difference between a Thermo Top and a Thermo Top S, and the 'S' model is more common.
The S model requires an external fuel dosing pump, whereas the non-S does not. The non-S is, instead, connected inline with either the carburettor's fuel supply, or the return of a fuel-injected setup.
And, critically, this specific model of Thermo Top, provided to BMW for factory fitment, has only 3 wires. Two large ones, power and ground, and the third smaller wire comes from whatever is controlling the coolant heater; whether that be an external timer unit or the climate-control unit or whatever. And it just supplies +12v whenever it wants the heater to run.
Turns out, it really is just that simple to wire it up.
Anyway, I've added an update post with the technical info to my 2016 thread, and am now awaiting execution, by humourless BMW owners, for thread necromancy.
But I had to get closure, you understand.
I don't want to be That Guy whose thread you stumble across, and come away never knowing if the problem got solved and how.