sounds like a fuel sending unit issue from your description.
see if this fits the bill.
Link Here!!that is for the
2001 - 2003 Chevy Silverado 2500 Fuel Tank Sending Unit for V8 8.1L
good luck.
by the way the issue may be one or more things to be honest. the fuel in the tank may be moving around and as it shushes from side to side the electrical resistance in the variable potentiometer of the fuel sending unit will either increase or decrease.
an example would be a full tank of gas will cause a floater attached to a lever to float to the top of the gas tank. now as the gas gets lower the level wil drop and so will the float. now remember it's attached to a pot so as it moves it's electrical value decreases. and the gas gauge reads the value as a fuel level.
if the gauge dose not move when the vehicle is idle then id say it;s just the gas moving around within the tank. it's worth a shot to test this before spending any money on it.
good luck.
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