What 70gtx440dana said is correct. You have experienced the smoldering before the fire.

Now is time for Good news/bad news.

Good news you know the problem but the bad news is that it it probably isn't just at that spot. I can almost guarantee that the end of that black wire where it attaches to the ammeter is starting to show overheating also. The wiring needs to be disassembled and checked.

I have in a pinch run a second wire alongside the original black and red wires inside the harness to take the load off them and prevent it from melting further. That works but to really repair the car right it needs to be pulled and replaced. See note 4 below

A few notes from my experience.

1. Lots of people will tell you to ditch the ammeter and swap to a voltmeter. I have never done it and after repairing the harness correctly never had a problem on dozens of cars. The Key is to make sure the wiring and connections are good and the insulators under the ammeter nuts are good. They degrade with heat and the bad wires/connections cause the heat that degrades them.

2. Place a larger than OEM wire in the harness to replace the Original Black and Red wires. Do this in the engine compartment and under the dash. Do not go crazy but at least 1 size larger.

3. Make sure that you use a fusible link at the Starter Relay junction to the main harness. I like to place on on the alternator also. Harness damage is caused by too much current and bad connections. If the Voltage regulator goes bad and sends the alternator into runaway mode, it happens a lot, all that extra current it is putting out will load the wires almost as bad a dead short in the main harness. The Fusible link at the alternator isn't required but is an added measure of safety.

4. Do not run the wires through the original bulkhead connectors. That is a known bottle neck. Those blade terminals are not good enough for the current flow. I use a pair of bolt in pass through terminals. It will not look OEM but it will not fail. When I can't get a good terminal I put the wire through a grommet and solder the engine side wires to the dash side of the wires. Shrink wrap and done.

If you have never pulled a dash it is not hard at all. Let me know and I will walk you through it.