Hi,
Check that there ''is an earth'' at the SW test point on the circuit board (goes to pin #6 U3 IC) when there are ''no headphones inserted.''
I realize that you said that you “Tested conductivity from the headphone disconnect to the motherboard and it’s good (so the speaker disconnect doesn’t appear to be stuck).” but I wasn’t sure whether you tested it back all the way to the IC.
If it tests OK then here’s an image taken from the [https://gamesx.com/wiki/lib/exe/fetch.php?media=schematics:gameboy_color_service_manual.pdf|service manual] for a Game Boy Colour showing the audio section. Hopefully it is the same for your edition.
[image|2305714]
(click on image to enlarge for better viewing)
Some things to check and do to try and isolate the problem:
Check that the capacitors marked with the green arrows are OK and not either open circuit or short circuit. For example if C38 was open circuit there would be no audio through the speaker. If C14 were short circuit it would shunt the audio from going through the speaker and if C27 were faulty it would affect how the audio amp for the speaker in the IC would function (there are two amps in the IC, one for the headphones and one for the speaker).
Unsolder the ''non earth side'' of the C14 capacitor so that it is no longer connected to the board and check if there is audio. If there is then C14 is faulty, replace it
Tap a wire from earth to the A-GND terminal that the speaker is connected to and check if there is audio. If so then the C38 capacitor is faulty, replace it
Replace the C27 capacitor and check.
If still no good you may have to replace the U3 IC audio amp.