Its interesting that the ammeter does not show signs of damage at its connections. The only concern will be if the shunt was damaged.

I think an ohmeter may be the best way to look for high resistance and poor continuity in the wiring. You can also use it to check for shorts to ground.

PS. Figure out what #18 on the bulkhead connects too. It's melted insulation suggests it got too much current. If yes, I'm seeing that right. Then its a clue where that excessive current was flowing too, depending on if the engine was running or not.
If the engine was running, then that will explain things too.