if the black wire is fixed to the sender unit, it's been bodged. Quite often on these senders, the earth fails and a fix (bodge) is to take an earth directly off the sender body rather than use the connecting plug.
You're right, you only need the 2 wires... the third wire is for an unused low fuel level sensor, you can see it here next to the float arm...
The revised dash models which were only available in the US in left hand drive had a low fuel level light but all UK spec cars across all 3 series didn’t have this feature. I’ve often thought this was strange given the cars appetite for fuel and the rest of the car being so well equipped for its day.
The fuel sender unit on the series 3 has 3 male terminals on it in a plastic housing and the plug from the car loom is also a 3 way but has only 2 wires going into it. The 3rd space in the plug is left empty.
I had a go at connecting the low fuel sensor up on my old car.....I got an old piece of loom with a female plastic plug on it, cut the plug open and retrieved the female terminal connector…. This then just pushed into and locked in place in the spare space in the terminal block on the sender wire. You can see the additional wire here in orange....
My guess is that if the fuel level drops, to say 1 gallon left, the sensor will go to ground and complete a circuit so if I connect a bulb or led to +12v that comes live with the ignition and the other end to this sensor, I should have a working low fuel light.
My thoughts are that when the new tank was introduced for the Series 3,( and the stateside GSL-SE) Mazda just used the US spec sender and ignored the fuel level sensor part of it as the UK cars weren’t wired for it, as they still used the old dash.