Thanks for the update.
For clarity, refer to the source of the problem as the
fuel level sender wiring, not the fuel float. Beemuker, a member here, is having a similar challenge; in these aging parts, it is becoming more common especially if corrosion from old fuel has been allowed to occur within the tank. He's attempting to replace a faulty sender with an ebay replacement.
He's following successful technique done by this rider. By all appearances, this solution will allow you to remove the OEM sender, analyze how it's wired and maybe even repair it eventually if a working OEM doesn't fall into your lap. In the meantime, you'll be able to ride.
When I first got my Brick, I carried a spare gallon of fuel with me, filled the tank then allowed my Brick's engine to start missing from lack of fuel. Using the tripmeter, I derived an average over four trips of mixed terrain riding. 224 miles is the point at which the engine becomes fuel starved on hills, so I always refuel at 210 miles or less. My fuel light registers at 170 but I ignore it unless there's a long stretch ahead without refill. That's one source of excitement in my life.
The odometer/tripmeter method works well; all that is needed is awareness.
Awareness is a major component of safe riding anyway.
Fix it the simple way being offered at the link I provided to avoid chronic
sender envy.