As far as I can tell from the manual, the gauge responds directly to the voltage from the sender unit, while the light is switched on by the ECM in response to the voltage from the sender unit. This implies that it's the sender that is at fault, but I'm not an expert and would be happy to be corrected.
Like all these faults nowadays, it might cost a bit, as the gauge is part of the instrument pack and the sener is part of the pump. Unless anyone out there has better experience/advice, this is probably one for Testbook and your LR mechanic. In the meantime, suggest you fill the tank, reset the trip odometer and fill up again when you get to, say 400 miles, depending on your driving!