I have a IIGS ROM3 that makes a chirp sound from the power supply when I switch it off. Otherwise, everything works fine. Its a Dyna Comp LR62786 power supply shown here:
https://stayornay.com/mac84tv/repair-guides-documents/apple-iigs-power-s...
I've opened it up and don't notice any buldging capacitors. I'm OK with doing the soldering work, where I struggle is ordering the correct parts. For example on the above parts list, I can't even find item #3 100uF capacitor with 7mm pitch that meets the space requirements listed. I can't find a capacitor kit for this power supply either.
Any tips on finding the source of the noise?
One other data point - the chirp occurs even when power connector disconnected from logic board (no load).
Per your tests, the chirp comes from the PSU itself. It may be simply a coil buzzing while the switching dies off. I wouldn't worry too much about it but one thing you could do is to reflow all the soldering joints on the PCB. Sometimes micro-vibrations may cause a crack in the solder, allowing the vibrating component to vibrate more and to generate sound.
As usual, please remember that in that power supply there are lethal voltages: I do not advise you to open and to work on it and you should not follow my recommendations.