@eaglepin, how did you make out ? Did you find the problem ?

Thanks for following up! TL;DR the machine rides again!

Everything was measuring as expected on the multimeter (thanks again for that diagram). I went through the logic of which circuits are tied together to make the pump turn on. I eventually came to the max-level probe, which should "tell" the brain box to turn off the pump if the boiler is full enough (so as to not overfill). That probe works by detecting ground, so I thought that maybe it might have developed corrosion or something from sitting dry for 3+ months after being repaired and tested.

So I disconnected that probe lead and finally I heard the pump relay click! The next issue after that was that the pump had lost its prime (which I only suspected from prior troubleshooting attempts with the machine vendor). So I attached a clean children's Tylenol syringe (haha) to the pump inlet and really rammed on it. Finally the pump kicked to life!

I then suspected that I would need to replace the probe or clean it at least, but for some reason after reconnecting the max-level probe lead, everything works as expected (including proper boiler refill, without overfilling). I would still like to understand why the probe lead needed to be removed in order to seemingly "reset" the system, but at least it's working. Maybe after the lead was removed and the boiler filled, it cleaned off dust/crud from the probe inside the boiler, and now it's fine? ¯\_(ツ)_/¯

I really appreciate the help and support from this community

Really glad to hear you tracked the problem down and fixed it. Nothing like the feeling of getting something fixed. Way to go.

I have a car with gremlins. I'm getting the impression the Strega is prone to gremlins.

Good work! It's amazing how one can find their way once they have a map.