Start with Guy's suggestion to open the tank and verify fuel level. If there is fuel, remove the rear cover to access the tank area.
Remove the dual float assembly for the aux. pump and low fuel. It will have 2 red and 2 black wires in a single plug.
Take it out of the tank and manually manipulate the lower of the 2 floats using an ohm meter to see if it is working correctly, or just turn on the S1 switch while holding the float up and see if your fuel light stays off. If the light still comes on with the float up, verify function with a meter. If checking with a meter proves the float assembly is good, the next likely culprit would be the float control module which is the small box bolted to the inner right panel inside the tank area, where the 4 float wires go.
A note about the float unit: The float can be rotated by loosening the upper nut. I have seen cases where the float was installed with the float touching up against the side of the tank, causing it to get hung up. This is why Guy suggested to look in the tank to see if the float is stuck against the side of the tank or not. if so, simply rotate it slightly away from the side of the tank.