... and that's why I have focused on the polarity of diode D1. I really do see it as an acid test. Maybe you would not mind, at this juncture, reviewing its function, as portrayed?
...

In your schematic (photo 3, post #19) there are two diodes acting as "OR" gates.

If relay 4 is ON, relay coil A is activated by current to ground through the top diode. So if relay 4 is on, coil A must be on.

If relay 4 is OFF, then relay 6 can control coil A.

Basically the "OR" function of those two diodes saves them using relays with more contacts, so they can use a smaller and cheaper device for relay 4.

Regarding your other more complex circuit, I still think you need to start drawing out the schematic. You're obviously smart and have already put in a lot of work so this extra bit of work shouldn't take you too long.

All the control electronics seems to run from the +21v DC supply from the bridge rectifier. So get a bit of paper, put a horiz line along the top for "+21v rail", a horiz line along the bottom for "ground rail" and start drawing out the branches. Each branch goes from +21v to ground, through whatever relays and transistors you have.

That is basically the way a machine's contactor diagram is drawn and it can make a nasty complex rats nest into an easy to understand diagram.

 

Yes, I've noted the "OR" gates, as has the other thread contributor, and they exist on both boards with the same function.

As to the more complex PCB, message received and understood. Schematic it is. I think I'll also need to test potentials to work out how the Aquastat should be wired, as you suggested.

If there are aspects of the circuit which still bewilder me, post schematic, I'll be right back, if that's okay.

Thanks again for your time and interest.