Had to get around to finding some new test leads. I swear I own 30 of them but they all ran away or hid in boxes.

Sorry it took time to get to and re-post.
As for taking apart the heat sink. NO. Not until I have a reason to. This is a difficult to get proprietary board with no schematic. To buy the board would be over $1800 USD if I can find one. As only one voltage output is not working the risk of doing damage by taking apart the heatsink is too high. Right now I can simply bypass the 12v rail with an inexpensive power supply if I need to. If I damage the board I lose that option as a backup. That's a hack though and I want to figure out what is going on.
I spent some time analyzing the board tonight with my multimeter and a bench power supply putting out 3v and .1A DC as a test current.
It looks like someone took several modular, independent circuits and married them on a circuit board for production purposes.
The high voltage side outputs 120vac and 80vac (servos). The machine is 240v compatible so I suspect something on the board handles stepping down from 240v to 120v, but that's not my focus right now. Could also be a different PCB for 240v. There are two RBV-1506 bridge rectifiers on the high voltage side. (see image)
There are 3 PCB Mount stepdown transformers that appear to be configured in parallell mode for 115v to their target voltages.
The board outputs +5, -5v, 12v, and 26v.
I have no idea what 26v is being used for, but it's not my concern at the moment.
The configuration of the IC's on the heat sink appears to be a fast recovery rectifier paired with a MOSFET. One pair that I can read is an NEC S20LC40 and a NEC K703.
Datasheet for the S20LC40 (fast recovery rectifier):
https://www.mouser.com/datasheet/2/366/J533_S20LC40UV-271056.pdfNECK703 Datasheet (MosFET):
https://www.datasheetq.com/datasheet-download/231726/1/NEC/K703Apologies in advance for linking to that awful datasheet-spam trap website. It's at least an NEC datasheet. The rectifier seems to have gone to China as a generic at this point.
My hypothesis is that each transformer is driving a power rail as an independent circuit with a common chassis ground. The only advantage I can see to this is good isolation / stabilization of your voltages. It's not how I would have designed it, but I'm sure whoever did this has more experience than me.
I believe the capacitor is fed from the MOSFET and rectifier. I'm not entirely sure how to check the mosfet and rectifier in circuit.
The next thing that makes sense to me is to get an isolation transformer and a variac and put some AC voltage in the high voltage sign and probe the transformers to see if my hypothesis on the circuit design is right. i.e. what voltage is going into the transformers and what is coming out.
Once I identify the input voltage I can turn the voltage up to 120vac to see what the output voltage of each transformer is. That will tell me which one is 12v (or not) and where my +/-5 and 26v are at.
From there I should be able to disconnect power and use continuity to see which rectifier and mosfet are involved.
I think the circuit design is:
Transformer-> Rectifier -> Mosfet - > electrolytic capacitor -> output diode
There should be some sort of sense/feedback loop for output voltage management. It may be sandwiched in the heatsink and not visible to me.
I think the electrolytic is there to buffer the switching voltage.
My questions are:
1) Is there a better way to trace and test this?
2) Am I headed along the right lines of circuit design or is there a different way I should be thinking of?
My expectation is that I will find a component that has failed somewhere between the transformer and the capacitor. It's possible the transformer has gone out as well.
NOTE: At the top I mislabeled the electrolytic capacitor as a transformer. Sigh. long day. We'll see who reads the whole post. lol.