Hmmm ... I had a look into how the low fuel sensor works.
It is a separate sensor than the float resister used to drive the fuel gauge. Its basically a thermistor - its resistance decreases as it gets warmer. When its covered in fuel, the fuel sucks away its heat so the sensor stays at high resistance, so it doesn't pass much current, so the fuel light which is in circuit with it hardly glows at all - not enough to be visible. When fuel level drops below the sensor position, the air around it doesn't conduct away heat as well so the sensor slowly heats up due to the current flowing through it, which reduces its resistance which increases its current which reduces its resistance and so on ... as the current increases, the fuel light glows brighter until its visible. This of course happens to a current limit, otherwise it would get so hot it would ignite the fuel vapour in the tank and its game over!.
The thermistor is mounted inside a can which has only small holes in it, such that the thermistor response is slowed and the light doesn't go on/off constantly when the fuel level is near the sensor level.
In your case, I'm thinking the sensor has moved and is positioned too high in the tank so its coming on earlier than expected. I've never actually looked inside my ('97) tank, but I assume there is some type of bracket the sensor is attached to? Maybe yours has come loose or is just sitting too high?