It sounds like you may have a faulty gauge or sending unit, because the gauges in all three of my 1966 Chevrolets would go from F to E. However, due to my previous experience with GM gas gauges, I rarely allow them go below the 1/2 mark. I had a 1970 Pontiac that would read 1/4 when full and 1/8 when empty. I ran out of gas several times with that car.