Open that fuel gauge and bend some thingy if you want . Just know you don't absolutely have to. When you pull that 3 post instrument from the housing look at its backside. You will find it is grounded to the housing. If you pull any other 2 post instrument you will find they are not chassis grounded. The ground link on the 3 post instrument is the ground for the internal limiter ( and one possible cause of limiter failure ). To interrupt that ground ( a layer or 2 of electrical tape over the little piece of metal they put on the back of this instrument ) disables the limiter completely. It cannot do anything good or bad if it doesn't have a ground.
The only good reason to open the instrument is to see what the thermal gauge part of it looks like. Don't be surprised to find it toasty. If there's a lot of black crud build up on that resistor wire,, If the bi metal beam has a bow at room temperature, its going to need renew service. It can't be cleaned.
The vendors of aftermarket regulators show pics of instruments that look fine. They do know what you "statictically" will find. I've seen fewer that 20 that looked as good and that is of the hundreds I opened during a 8 year period.
And about your "black wire" question... There's a contact pin missing from your board. that is one side of the brake warning lamp wiring and one of those is in fact a black wire so I can't know for sure if you're inquiring about that one of the noise cap' wire. As others have said, you can delete that noise cap' when using a solid state regulator that generates no noise. anyway... that is the 12 volt post ( blue with white tracer is routed to there ). The 5 volts out of your regulator can go where the black plastic cap is but if the wire they provide is long enough, route it to the next one down in that path/trace so you can leave that plastic cap in place. It was put there for a reason. Hope this helps.
