I picked up a Rollergames (System 11C) recently and I want to design my own, here's what I've figured out. This may or may not apply to earlier System 11s.

On the audio board, all the signals get mixed together and fed to a buffering op-amp. The output of this is wired to one of the pins on the volume control header. The signal goes to the volume control pot next to the tilt bob on one wire then comes back on the other. This return signal is what gets fed to the speaker amplifiers.

You can tap into the pre-amplified audio signal at the volume control on the side without the resistor and audio ground from the shield of the volume control cable.

I tapped the signal and ran it through a 10uF capacitor and 1/8" audio jack, then plugged it into a headphone amplifier. Worked great.

Note: this doesn't affect the existing speakers at all. Eventually I want to add a switch that disconnects that audio return line.

Shield is the outer connector on the cable, usually made of wire braid. It's silver on the volume cable.

Kind of hard to see where I got audio ground, it's connected where the resistor and volume cable shield are connected at the screw lug.
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For testing I used a regular 1/8" stereo plug wired up mono, 10uF electrolytic capacitor on the signal line. Your plugs will depend on your amp.

My test amp is a powered bookshelf speaker, it has a headphone output. You're looking for a stereo headphone amplifier.

Yes, something like that, though that looks like it also doubles as a speaker amplifier.

On this one, you'd need to connect the audio signal from the machine to the two RCA jacks labeled LINE INPUT.

I am trying to source a 1/4" stereo headphone jack with a NC SPST or SPDT isolated switch, like this. The preamp signal from the machine isn't meant to drive headphones directly (though you probably could in a pinch). The switch would route the signal between the headphone amp or the sound board amp.

switched jack (resized).png

Definitely could use one side of a DPDT. I've only searched eBay so far.