that black wire has a welded splice where it branches to several places. One branch goes to the ignition switch. At switch on it feeds a portion of the fuse box. You lost radio, wipers, signals, that portion of the fuse box, so I suspect you have another problem. Melt down at the amp meter is/was failure at the weak link. It's rarely the root problem. Have a look at a white plastic harness connector under the steering column. These multi wire connectors melt down to cause short/crossed circuits.
I have a good used amp gauge and other parts for you, but to toss it in there and toast it too is not a good plan.