The low fuel light is actually a warning light so you don't run the gas too low and fry the fuel pump. This is from Kevin. If it's staying on it may be sticking for old gas. Fresh gas may eventually loosen it up. the thing is totally simple. there is a ring of some flotation material around a shaft. The ring of material slides up and down the shaft as the fuel level changes. When it touches the base of the shaft, it closes a connection that turn the light on. In it's normal operation as it's set up it should blink on and off most of the time once it starts to touch the base as the splashing fuel will keep it jouncing around. There is no physical connection to any other part in the tank or AFAIK, any other component in the system.
You can run a tank of gas or two through it and see if that loosens it up, or you can remove it and clean it, or see if it's actually broken. There is no gasket on it, per se, so be sure to use some thread sealer on it when you replace it!
As for a trip meter, I use a black erasable marker and write the fill up mileage on the chrome handlebar bracket.