Instrument cluster wiring

The top photo is correct. If you look closely your cooked circuit board still shows the R where RED was marked. The original wire had red casing. The solder, heat shrink, red tape, and cooked board you have there shows this has been a problem before. I think at very minimum you need another amp gauge. Some of them are better built than others. The posts were swedged into a brass bar for a shunt. The resistance can be in that.
Meanwhile you could just clean those wire terminals and put them both together on just one of the gauge posts.