I can tell you from the wiring on my 71 300, that the relay uses the voltage on the sender side of the guage to trip the relay, which sends power to a lightbulb in the speedometer that says "Low Fuel".
An LED would use no real power to speak of. It Probably it would take less power than the old relay needed to trip. I think they just have a simple circuit (with a zener diode?) built into the gauge to trip the LED when the voltage drops below a certain value.
