If it is a stereo jack, I am guessing it should be 2 channels of audio and 1 ground. Otherwise 1 channel and 1 ground. You have to see how the wires are connected on the male jack or test with a multicet.
When the two rear pins are measuting a short, it will be the connections like given in post #2.
When you put in a plug, the connection will be open in this case.
If there is no connection between the pins, it is a stereo jack.
I’d go one step further and test the connections in a stereo plug to the jack. Each plug connection should have connectivity to one and only one jack terminal.
If your plug has only two connections, then one of them should connect to one and only one terminal on the jack. The second connection will likely connect to up to connections on your jack.
Wire accordingly. One more point. One of the jack connections is connected to the jack casing. Use this as ground.