I am pretty sure that model has the notorious BMW Fuel Strip mechanism in the tank rather than a traditional float. BMW extended the warranty on these to 12 years because they continually fail. They never provided a fix, just a warranty replacement with the part that is known to fail. It is the microscopic resistive wires in the flexible strip which fail, nothing mechanical and nothing in the regular wiring harness.
My 2007 GS Adv has been through five (six if you count the one that was DOA when the dealer installed it). The last failed this Spring just after the warranty expired. I now just reset the trip odometer and the fuel mileage every time I fill up. The fuel strip is almost $200, not counting the charge for dealer installation and computer calibration. So, probably $400+ for a replacement with a full expectation that it will fail again in short order.
A guy in the Netherlands has supposedly worked up a way to use a later model float and recalibrate the computer to match, however you need to buy those parts, plus an Android phone, the app to fool the computer, and adapter cables from the phone to the bike. I just built a resistive circuit to trick the Low Fuel warning light circuit and live with the trip odo.