Attachment shows the locations of the two relays, in a modified version of the wiring diagram from post #1. Each of the two Solid State Relays ("SSR" devices) supports load current of up to 25 Amps, but they are not the same.
The AC relay is on the right, labeled "B". (It interrupts the "Hot" 120VAC lead coming from the "dumb thermostat"). Don't make this connection too close to the heater, within the heat resistant "BLU" wire; try to put it at considerable distance so that the relay doesn't get cooked by heat coming down the wire. (I don't know where the junction between "BRN" and "BLU" occurs; but if it is easy to access, then that would be a good place.)
These relays get warm when they're switched too often, but that doesn't happen in this application. No heatsink is needed here.
The harder-to-find DC relay is labeled "A", and occurs along the the +12V "YELLOW" wire from the selector switch. As with the 120VAC "BLU" wire, cut in at a location with considerable distance from the from the heater.
Good accessibility assures that you can bypass the relay, if the control system blows up during a trip. If you put both power leads on the
same "load" contact of the relay and tighten the screw down, then the circuit is always "on" -- no matter was has gone wrong inside the relay, or back in the PID. (If you want to be strictly "proper" about your emergency wiring, you'll use a small terminal block like #2 -- one lead per screw terminal, never two.
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The last issue, which I have not covered until this morning's edit, is the relay control wiring. I am not sure whether they should be wired in series, or in parallel. (I'll guess that either way works, but I'll be testing it the bench before I wire it up in the TM.)
The question is whether to wire the SSR control leads in Series (through each other), or in parallel at the PID controller.
Probably, BOTH ways work, but Series is more simple. Both SSR devices images on the website show a "switch on" voltage of 3-32V, and the PID controllers dish out 10 volts. So, unless the internal resistance of each one is badly "out-of-whack" versus the other, they'll both be seeing enough voltage (across the control leads) to make the switch.
Sorry, editing this post has DESTROYED the description of parts (which was here when I finished last night). That parts list and discussion
(the MEAT of this whole Thread !!!) is now below, in
post number 12. Grrr, must have coffee
first, before tearing big things apart without verifying that I've made a viable backup copy.