Just a quick sanity check here. I've a car radio with built in phone bluetooth capability. There's the option to install an additional microphone to improve clarity.
I ordered a little mic online, but it has a stereo 3.5mm jack and won't work with the radio. I tried the radio with a mic with a mono jack and it does work.
If I short across between left and right channels on the stereo jack, should it then work with the radio?
An electret mic has a Jfet inside that must be powered.
Some electret mics have two wires, the ground wire which has the source pin of the N-channel Jfet and the signal wire which has the drain pin of the Jfet that needs a few volts at 0.5mA through a series resistor.
Other electret mics have three wires (it is a mono mic), the ground, a few DC volts to the drain pin and a signal wire which has the source pin that might need an external resistor to ground.
Maybe you have an electret mic with three wires but the radio is designed to use a two wires mic.
Assuming the socket provides power and the mic uses electret capsules, it will still work if it has two mics (= really stereo) and they are joined in parallel. Technically it really screws up the current each can draw but for use in a car where quality isn't important it should suffice. If you are lucky, you may even get some noise cancellation effect if you can position the mic 'just right' so your voice is only picked up by one of the mics.