That would appear to be a 10 SI one -wire alternator since there are no wires going to the internal regulator terminals in the top of the alternator.
The large red wire is the power output wire from the alternator and it must go to the original junction of the battery, alternator, regulator, and cab feed wire.
This is the original wiring for the 67/72 trucks. The one-wire alternator doesn't need the harness from the regulator so it can be unplugged or left plugged in, either way it has no purpose and will not affect anything except the points inside it will close and stay closed as long as the key switch is on. Therefore it should be unplugged.
Notice the two small black wires in the diagram, these are the battery gauge wires and they have a small 4 amp fuse in each wire to protect the gauge. The wires start at the battery junction on the passenger fender and at the main junction I described above.
They run through the firewall to the instrument cluster plug to pins 1 and 12, and then to each side of the battery gauge. They are both positive so no grounding except for the gauge itself, is needed.
The fuses are easy to spot in the harness and are located in the wiring that runs over the radiator and in the harness below the left headlight, at least that's where they usually are.
This should give you some information to help solve the battery gauge inop
problem and hopefully it explains the alternator as well.