Where does this connect

The three pins right there next to it and with the one that is covered by the cap IS A CLUE. You have a Ralley cluster which means the pulsating instrument limiter/ regulator is inside the fuel gauge. One of the remaining two pins is the sender, the other is the +12V feeding into the gauge housing which connects to the limiter circuit in the gauge. The capacitor pigtail connects to that stud which reduces radio noise. You can determine which one by looking up the wire colors to the cluster connector. One will be switched 12V and the other will be the fuel gauge sender.

Also make certain of a few things Is that the replacement (used) board?

Make certain the harness connector pins are not corroded/ loose at the crimp at the board. Clean, flux, and solder them. Loosen/ tighten all the gauge stud nuts. Find a ground point for the board (follow the instrument illumination lights) and make a ground pigtail so you can bolt the pigtail to the column support or dash frame.