Mike,
Sorry to hear about your wire. Good that you can move fast!
Using the Service Manual (SM) diagrams, I've compared my 3B harness to the 3A. At the starter it seems very similar. The only real function I see to that wire that goes to the Ammeter is so it can register Amp draw (negative when you hit the starter rod and positive when the engine is revved).
On both, that terminal on the back of the gauge shows just 2 things connected: The + wire (after passing the starter) and the horn (it needs to be hot always vs. switched).
The other terminal should have a wire that runs to your ignition and the other wire to the regulator. All wires need to be insulated from the clip that holds the gauge up against the "dash."
It may be possible there was a grounding on that wire. It may be possible the starter pulled too many amps and overloaded the wire.
Before you disconnect, using an Ohm meter, check to see if you have continuity from the end of the burnt wire to the metal body, i.e. the bracket holding the gauge or the back of the dash somewhere on bare metal.
You may want to test the starter (I'd take it to a shop so they can put it on a machine).
