Fuel gauge

make sure you fuel tank cap is shut tight, if not you will get false reading,

)  I THINK the problem is that the way the system is set up, the car drains the passenger side tank first.  So the passenger side electrical fuel level sensor is constantly being exercised over its full range of motion.  The driver side tank is the last to be fully drained so its sensor tends to be exercised over only the upper part of its overall range of motion.  Thus the sensor's electrical windings in the potentiometer do not get a cleaning wipe by the pick-up very often.  I THINK the result is the lower portion of the potentiometer develops some kind of contamination that effectively shorts most of the lower windings together.  So as the fuel level drops the potentiometer wiper gets shorted to ground.  The computer then thinks the tank is empty.   Regardless of the cause, research on the various Corvette forums (and as experienced by several club members) indicates 99% of the time that this problem crops up it can be solved by adding a bottle of Techron Concentrate Plus to your next one or two fill-ups.  Be sure you get the Concentrate Plus; it is available at better automotive stores.  As I understand it, chemicals in the additive clean the deposit off of the fuel level potentiometer windings.  If this does not work, try GM's additive (more expensive as I recall).   If those efforts do not fix the problem then the fuel tank will need to be opened up and the sensor replaced.  I recommend a GM dealer for this work because special "exact torque" screws are used to prevent over tightening and stripping out the threads when closing the tank.  A poorly trained mechanic might use the wrong screw resulting in under tightening (and a leak) or over tightening (stripped threads and also a leak).