The reason I mention it is that the SAE ends of the adapters I have are not marked with polarity, so I'm not sure which pin or hole connects with the ID or OD of the coax plug and socket, and I haven't confirmed with a tester yet.@Larry Fine , just remember the connector as shown in your adapter photo 1 is always from source power. The covered pin on an SAE connector should also represent source power. That is so that any pin with power on it that may be unplugged is not exposed resulting in potential to short out against something like frame or you.
I don't know whether the Heat Demon controller is polarity-sensitive, but I err on the side of caution and presume it is.
Speaking of which, I know of someone who is selling a bunch of them (see post #29) for $20 shipped. Let me know if anyone wants the contact info.