Thank you!That's just an off the shelf connector with an SMD capacitor on a small PCB. I am a huge fan of the Rean version of the TA4F, 1/3 the price of the original Switchcraft version and much more robust (including water-resistant varieties) and a better latching mechanism.
If this is like other microphone terminations, you have shield on Pin 1, Bias coming in on Pin 4, shorted to Pin 3, and a resistor or capacitor hopping between Pin 4 and Pin 2. It looks like your mic is an SMD tantalum capacitor, 10mF 16V but any equivalent capacitor would work to smooth the voltage, doesn't need to be an SMD on a board.
Probe the board with a continuity meter to make sure what I think is the pinout is a pinout, but that's generally what I do to re-terminate TA4F microphones.
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