No doubt on this one. The fuel pump needs a new level sensor. There are small metal fingers that move with the float arm across a metal grid on a printed circuit board that will indicate the fuel level. Those fingers wear and you get inconsistent readings. Very common failure. You can purchase the level sensor separate from the pump. Not sure on the LeSabre, but my Bonneville had an oval shaped access panel in the trunk to get to the fuel pump allowing you to change the sensor in well under an hour. Without the access panel you have to drop the tank.
Or, just keep track of the miles you drove since the last time you filled up with gas.
2001 Bonneville SSEi (retired at 365,000 Kms.)
2014 Jeep Grand Cherokee Overland (yes, I know its not a GM)