A DC motor (all DC motors from fans to toy trains) rotate faster as the voltage increases, or slower as it decreases. They also rotate backwards if you reverse the polarity (+ with the -, and the - for the +).
Now you can reduce line voltage by adding resistance to the circuit. In the case of a toy train or your gas gauge sending unit it utilizes a rheostat (some ni-chrome wire wrapped around an insulating form that has a contact point that sweeps across the windings to vary the voltage). In the case of the toy train it controls the speed of the locomotive by varying the voltage to the DC motor. In your gas gauge the float moves the rheostat arm depending upon the gas level that reduces the amount of voltage that goes to ground. As the resistance increases to 60 Ohms (more windings) the voltage to ground drops and the gauge reads empty. At the full nominal voltage of 12 Volts to ground (few windings in the circuit it reads full. If you have a bad ground (with a lot more resistance than 60 Ohms) then it will always just sit ther at empty and laugh at you!
DC circuits are extremely easy to understand if you understand the function of resistors, batteries and the concept of a switch or load. In fact it is as easy as PIE (the letters used to express Ohm's Law) that is used to calculate values to predict what the reading should be ahead of time. Or allow you to correct or tune a circuit to make it behave as expected (say you are trying to use a 12 volt battery in an older than a 1955 Chevy that used a six volt battery for everything). Plug in a 12 volt battery in a six volt car and your volt gauge and your gas gauge go up in smoke though your head lights are much brighter till they also burn up.
From your description of the problem you have either a bad switch or a blown (burned open) resister. My money is on the switch being bad as it isn't feeding any power on high speed. My guess is the contact points in the switch have burned away and are not making contact to complete the circuit.