Onto the audio section! This section assumes that you have made the connections outlined in the "Wiring (Rear Case)", which are: The power connections for the amplifier and, the amplifier/speaker OUT connections to the Main Connector.
With the Game Gear's original headphone jack, the two 'Headphone Detect' pins are open circuit when no headphones are inserted, and closed circuit when there are headphones inserted. The other pins are self explanatory, audio connections.
We're going to pass the amplifier's SDWN pin and the 'output' from the headphone detect to the Teensy on the front panel through this two pin connector. The Teensy will have it's INPUT_PULLUP turned on for the headphone detect pin. When it sees the pin go LOW, it knows that headphones have been inserted, and it will drive the SDWN pin low, which will turn off the amp. Otherwise, the SDWN pin will be driven HIGH, activating the internal speakers.
When connecting the RasPi Audio to the Amplifier & Headphone Jack Chain, add a three pin male header/three pin female header connector, so that it can be quickly disconnected. This will also allow you to create an audio test cable, so that you can pipe audio into the circuit once you are finished. You can use any 3.5mm male cable, or old pair of headphones to make the test cable.
Raspberry Pi Audio GND
MAX98306 Audio GND (L-/R-)
Here's the audio test cable, you can plug this right into your three pin header to test your audio circuit. Match the of your headphone cable to the pinout of your three pin disconnect.