Best Of

" I have to admit to being confused by the schematic, it seems a lot of those paths are on the circuit board and I'm reluctant to fool with a $1000 board. "

Many folks are, so the best method of chasing out an electrical defect is abandoned for just guessing. And often that does not work out very well as your are sadly finding out.

You should not have to fool with the circuit board, just take voltage measurements at strategic points at the connector pins (back probing), however I am not convinced I'm looking at the correct wiring diagram for your unit, so making recommendations of connector pin designations is difficult from here.

As far as your Yellow arrow I believe that is a dual temperature sensor (a thermistor) where the Yellow wire is the common between the two sensors. The sensor could be bad, intermittent internal connection to its leads. An Ohmmeter may be used to test the sensor. Also the pin fitment of the connector pins may be poor so the pins in the connector do not touch the sensor pins correctly. Careful inspection may be needed. Also the crimps to the wire(s) could also be defective. Connector pins can be replaced, the hard part is identifying the correct pin and most folks do not have the correct crimping tool.

I believe the Orange arrow is another single temperature sensor.

To me, the thing is, if the sensor or the connection to it were bad I would thing that would produce an appropriate error message about that sensor. And possibly the temperature readings in the 'Status Display Screen' would not be reasonable.

*** However right next to it (Red circle) is a jumper that I believe has to be intact to supply power to the Gas Valve. I would be very curious about its integrity. ***

" While I was jiggling this connector it started to fire and I heard a clicking sound coming from this device on the side of the heat exchanger: "

This looks like a ceramic power resistor and should not make any clicking noise. Possibly it is a another temperature sensor or limit switch.

Basically only relays, solenoids, Gas Valves make clicking noises, I suspect you were hearing a relay click from the control board.

" Can it also be I'm chasing a bunch of old connections that are accumulating in low voltage? " This is possible but I don't think it is the cause in this case, since they would all have to heal for it to work and it does work once in a while.

Since you previously identified severely insufficient voltage going to the Gas Valve assembly (rectifier board) during an ignition attempt. I don't believe messing with the throttle will prove anything more beneficial than adjusting the throttle on a car when troubleshooting a dim headlight.