Hi there, I had the same problem a while back.
Your fuel guage sender is faulty
When your sender drops to a certain level it becomes open circuit either because the wiper of the sender loses contact with the resistor or the resistor is rusty.
The best way to fix it in my opinion is to replace the sender.
From memory, the resistance of the sender circuit when the tank is full should be around 90 ohms and near to 0 ohms when empty, or the other way around , can never remember.
In any event if the resistance is any more than 90 ohms you have an open in the circuit somewhere, my guess is the sender.
Hope that helps