Hi,
Anyone know what contact this is? Which female cable part should I get to fit that?
It looks like a "special".
Auto electrical companies delight in them, & I doubt if you will find the female part by itself -----maybe you could pick up one, complete with a length of wiring harness from the auto wreckers.
If you just want to connect to the pins, you could use individual ordinary auto "push on" connectors.
Another thought is to make a body up with a 3D printer to hold the above type of connectors securely, & mate correctly with the male plug & recess.