Have you done any continuity tests on the 6 pins in the green area? Both with a plug in and without? That would help to identify the functionality of the jack. It could be that two sets of those pins inside are connected by a switch. When you have nothing inserted in the jack, those contacts short out and cause the signal to come back out and go somewhere else. However, when you have a headphone plug inserted, it will break the connection on those pins, and keep the signal sent to the headphones. This is how AC'97 audio works for computer speakers.
Here's what to do. Take the second picture, label the pins 1-2-3 across the top and 4-5-6 across the second row. Then take continuity measurements from every pin to every other pin. Make a table like so:
Pin 1 to pin 2:
Pin 1 to pin 3:
Pin 1 to pin 4:
Pin 1 to pin 5:
Pin 1 to pin 6:
Pin 2 to pin 3: (you've already done pin 2 to pin one above, no need to do it again).
etc.
Tell us for each combination whether you have continuity or not. Try this both with a headphone plug inserted and without. Also, if you have a headphone plug with bare wires on the other end, you might be able to check the pins against those wires.
