This is the wiring block from the rotary mechanism:
The connections are as follows with the dial facing down with the wiring lugs at the top, from left to right they are yellow, blue, white, and red.
Blue, white, and red are open when the dial is at rest, and closed when the dial is rotated.
Yellow and blue are normally closed, but pulse open N times when the number N is dialed (10 times for a 0).
Blue and white are connected together by default, and will probably be used as a common ground point Since blue and white are shorted when the dial is rotated, the blue can act as a ground with yellow and red being used for GPIO connections on the Pi. White can remain disconnected.
I’m considering using the red line as equivalent of the push-to-talk button, since I don’t have a better solution at this point. The alternative is to either add a button to the phone (which will ruin the look), or remove the need for a push-to-talk button altogether, which is technically challenging, especially if I’m hoping to operate in the relatively noisy Maker Faire.