Sounds like the sending unit might be bad. You stated that the gauge moves to the extremes if you open or close the circuit. That tells you that the gauge is working as expected. And if you're closing or opening the circuit by grounding and ungrounding the wire that connects to the sending unit, then you've verified the entire wiring of the circuit.
The rheostat on the sending unit is a variable resistor (the amount of resistance is controlled by the location of the wiper arm on the rheostat), and the total resistance of the circuit determines the location of the gauge needle. If the needle never goes above 1/2, there are several possibilities.
To troubleshoot, remove the sending unit from the gas tank, connect its flange to ground (either clamp it to ground or wire it to ground) and then operate the sending unit manually. If the gauge goes to full when the float is all the way up and goes to empty when the float is all the way down, then the electrical part of the sending unit is working properly. If it doesn't, replace it.
If the electrical part is working correctly, there's two possibilities that I can think of. There's extra resistance in the circuit somewhere, or the float is bad and never rises to the top. The former is possible. The latter happens frequently. Floats get soaked with fuel (if they're made of absorbent material like cork) or they get a pinhole opening that takes in fuel and makes the float heavier so that it floats below the surface instead of on it.
Too much resistance can be caused by bad wires or bad connections. Sometimes fuel gauges don't get a good ground through the tank and need to have a ground wire connected directly to a flange mounting screw.
