A single wire from a round object is a noise supression capasitior. It's duty is to prevent a pop noise in your radio speaker that is generated buy thelimiters points, opening and closing. A solid state regulator doesn't generate the noise so the capasitor isn't needed.
But wait... That wire should have been attached to the limiter. Why would it be attached to the fuel gauge unless your limiter is infact inside the fuel gauge ?
If that fuel gauge has 3 posts, you wont find a limiter attached anywhere else.
All this and more is available to read on the DeMonIVR website.
