It's not rocket surgery.
Use the toilet model again. If you bend the arm down, it cuts off sooner. Why? Because it is indicating that it is full even though the water is not as high as it was when the arm was straight.
If you bend the arm up, it fills up more because the float isn't being lifted up as soon to indicate it's full. Heck, if you bend it up enough, it won't cut off because the water will go down the overflow since the arm won't go high enough to activate the cutoff.
So if the gauge is reading empty at 9 gallons, the float on the sending unit is higher than it should be (or there is some other problem that we don't know about).