According to the wiring diagram it's a variable resistor. I don't know for sure on the 'Bergs but on many bikes it's a thermistor, i.e. a resistor whose resistance varies according to temperature and it works because the fuel keeps it cooler until the level gets too low and the thermistor is uncovered, at which point it warms up slightly, and the resulting change in resistance is enough to trigger the light.
Having said that, there is a specific symbol for a thermistor and that's not what's shown on the wiring diagram, it just shows a simple variable resistor which would require movement to make it change it's value so maybe this one works on some kind of float or by measuring resistance through the fuel. Actually, given the reports of boiling fuel you'd wonder whether a thermistor wouldn't end up bringing the light on even when there *is* plenty of fuel left!
Either way, its resistance should drop when the fuel falls below the sensor but I have no idea what the values should be before or after. Maybe someone has had this problem before and taken measurements?
First check the indicator bulb's ok, and that it hasn't pulled back out of the mounting tube and is lit but hanging down behind the speedo unit out of sight! Then you could check that you have 12V on pin 1 of the sensor plug (brown-orange) and 0v on pin 2 (brown). Pin 1 comes through the indicator light so it might be dropping a little voltage if some current is drawn through the bulb which would mean it could be less than 12V, but if the bulb's not lit it shouldn't be dropping much. Pin 2 goes to earth so it should definitely be 0V. You'd want to check these with the plug connected to the sensor if you can. If you can only check with it disconnected it won't tell you as much but I'd then expect the full 12V on pin 1 as there should be no voltage drop across the bulb, and you could do a resistance check from pin 2 to the chassis which should be essentially 0 Ohms.
If you can't see any problems with the wiring and the indicator bulb looks ok, maybe your dealer can get you another sensor so you can try swapping it over?