I don't know the part number. But, it is a simple 6V regulator (7806) that can handle voltages ranging on either side of 12v. No, the regulators only need an input voltage and ground to work properly. These type of voltage regulator are commonly used on all sorts of electronic devices to step down and clean up input voltages. I have used them many times on all sorts of electronic projects. The by product of the voltage reduction is heat and that is why I mounted it on an aluminum flat bar (1/8" thick by 1/2" wide by about 2" long).
So, one red wire is input (left when regulator terminals facing down), one red wire is 6v output (right) and black wire is ground (center).
using a regulator will keep the output rock steady at 6 volts regardless of what happens to the input voltage. The result being a steady fuel gauge needle (other than the sender float moving up and down...which I would love to dampen out...hmmm).
Take a look at
this photo of a "Runtz" style voltage regulator and you can begin to see it is exactly what I fabricated. The "hole" is the output terminal, the screw lug is the input terminal and the black wire is the ground. The regulator is under the blue heat shrink tubing. There might be a capacitor (filter) or two hiding under the tubing as well. Debatable whether or not a cap is needed. If the power output fluctuates, I will add a cap between input and ground and possibly even output and ground as well. But, I don't think caps will be needed (remember, old fuel electric gauge technology...not a modern sensitive electronic gauge).