This black wire appears to have come out of the connector picture but i dont know which slot. There is an empty slot but it does not have a prong in it like the others so I "assume" it shares a slot???
At the top of the home page, look for Mustang Data. Click on it and you will see a link for wiring diagrams.. Click on that link and you will see links for wiring diagrams that pertain to your year, make and model..
It goes to the fourth hole on the side of the thick black/green wire. What's broken is the ground wire. That should be a male pin, but the tip of it doesn't look right to me.
You're probably best off replacing the turn signal switch (or finding a used one and splicing in the black wire into your connector).
They were originally riveted, it won't take much to pull a tin/lead solder connection apart. Silver solder will have a better chance of surviving, it is much stronger.