Yamaha Organ

At the Yamaha support FAQ webpage there are some suggestions:

https://faq.yamaha.com/usa/s/article/000001357

Didn't really help much. I have the owners manual, it assumes the sound is playing. I don't have a speaker setting or switch, that was the first thing I looked for.

Still, the only sound I can get is from the headphones.

I am presuming you have checked for this:

After Unplugging Headphones There is No Sound Description

Last Update: 1/8/2016

Digital Pianos: After Unplugging Headphones,There is No Sound.
When unplugging the headphones, the quarter inch headphone adapter may have been left in the headphone jack. When removing the headphones, the adapter (seen below) must also be removed.

Yup, noticed that first thing.

I am an engineer.

Just askin’.

We don’t have a lot to go on. Perhaps someone will come along who has the same electronic organ from 1988 with the same symptom.

You 'want to hear the sound through the speaker and not from an earphone'.. then why not plug-in and connect a loud speaker(s) instead of an earphone? An earphone is just a miniature version of the speakers..

If the sound coming from the speakers is not loud enough, you may need to use an amplifier, like thru your stereo set..

In such case, all you may need is a stereo patch cable that can connect and adapt the organ output to the type of signal input of your amplifier...

Impedance matching for the organ and an amplifier in my view should not be of a problem for an engineer like yourself...

Assuming it does have a speaker, the mechanical switch on the headphone jack could be corroded or bent or broken so that the speaker circuit is interrupted. Maybe spray contact cleaner in the jack and plug & unplug the plug to see if mechanical movement will renew the switch continuity. Try turning the volume up high so you might hear if you are making any progress.

At that age, electrolytic capacitors are known to dry out, perhaps presenting high impedance paths to the audio signal. This would require disassembly. Or just plug in your 1970s guitar amplifier and listen that way.