What is to the right side of the gauge? Full or empty? Inside the fuel tank is a variable resistor with a float attached to a rod. As the fuel level changes, the resistance (and voltage) changes, making the gauge needle point to a new value. If you remove the wire to the gauge, what does the needle read? Some dash gauges have a voltage regulator to make sure the gauges read properly. If you have one, it might have been zapped by the shorting of the batteries and it's making the fuel gauge wonky. Further exploration is needed. You can Google many sources of troubleshooting a bad fuel gauge or sender in the tank.
Bob & Donna
'98 Gulf Stream Sun Voyager DP being pushed by a '00 Beetle TDI