1. You don't say what the gauge is doing. You just say trying to "get the gauge working".
2. There are many issues that cause a gauge to "not work". It's not always the gauge.
3. A resistor just reduces the voltage to 6V.
Don't know what or how you tested the gauge but you say "12V going in and nothing coming out"......in and out of what? I will assume you know how to test for voltage. I will assume you tested the "Runtz" while it was hooked up to the gauge and the ignition was on. I will assume you realize that one side of "Runtz" will be approx.12V and the other will be approx. 6V. If you somehow are trying to test the gauge and are looking for an output voltage, there is none.
It's probably better to start a post with "my gas gauge is showing.........." What should I do?" Especially if you are not experienced.
These gas gauge issues come up all the time. They are usually a ground issue. They can be a sender or a gauge issue also. They can be a power supply issue. They can be a broken wire issue. They can be an empty tank. Could be a "Runtz" ground issue.
As you can see by looking at the resistor you bought, it has a screw and nut on one end. That is where you attach your power wire with a ring tongue terminal on it's end. Screw them together. The other end is for the gauge power stud. A resistor has no polarity and it can be installed either end to either termination.
A Runtz is a solid state voltage regulator. Runtz is a brand name that we should not use because there are many brands and the name is protected. Anyway, this type is usually made using a TO-220 package ($1). It has three leads. It has good accuracy and built-in thermal overload protection. The three leads are: input, output and ground. The accuracy needed for our gas gauges is debatable. The thermal over load actually saving a gauge from damage, is debatable.
So anyone's choice: A $6 resistor or a $20 regulator.