We can consider ground and negative the same thing since there isn't a neutral/earth/ground. Even if you look at it this way... positive is positive until some current is consumed.... where in a light bulb does positive end and negative begin? Where the electrode meets the filament? That wouldn't apply at the amp gauge since it doesn't consume current. It simply reacts to current flow. If those 2 wires weren't different colors, they would surely get hooked up reverse, and the instrument would react in reverse.
Lets just be thankful there are different colors. Imagine what if all wire casings were black? We would all need more knowledge to simply hook up a battery.
If your added red wire is tied to the same source black wire that would work. I can't know where someone might have attached it before. Does look like their crimped terminal pulled off from wherever the put it.
It was spliced into the lead of the noise suppression capasitor. If you cut into that little lead you will find that isn't a copper wire. Its steel or something ( not sure really ). Why it isn't copper or what difference this makes goes beyond my electrical knowledge.
A solid state regulator doesn't make electrical noise so the noise cap' is no longer required. You would have to ask whoever supplied the solid state regulator package, "Does the noise cap' make a difference?" I say this because some of the fancier solid state units have built in fault sensing with LEDs that flash fault codes. It may see the noise cap" as a fault. Sorry I don't have every answer.
One more point to mention... the original limiter is/was supplied from the ignition switch. The only fusible link, other than the main one out at the bulkhead, is/was that narrow spot in the copper trace. You have opportunity to add a inline fuse holder before your solid state regulator.
Necessary? If the OEM engineers felt there should be a point of safe failure somewhere, I wont argue with that.
For what its worth... The rally inst' panel has it voltage limiter housed inside the fuel gauge. Inside that gauge is also a tiny length of wire that serves the same purpose... A engineered point of safe failure. Better than frying wires back to harness connectors or all the way back to the ignition switch connector in all cases.
We have seen dash harnesses burned from here to yonder but that isn't common. Their engineers did go to some effort to control the damage caused by the possible/somewhat predictable faults.