The resistor goes in the line (in series) with the voltage feed to the guage. It's purpose is to drop the input voltage to the guage from 12 volts down to 6 volts. The guage itself has 2 coils inside that work in opposition to one another. The "limiting" coil pulls the guage towards empty, and the "operating" coil pulls the guage towards full. 6 volts enters the guage and is connected to one end of the "limiting coil" which is connected in series with the "operating coil" and then to ground. If you applied 6 volts to this arrangement the current flows through both coils and then to ground, but the guage would read "full" since the operating coil has more windings than the limiting coil. Now the sender, which is nothing more than a 0 - 30 ohm variable resistor is connected at the juncion of the 2 coils. As the tank level goes down, the resistance coming from the sender drops (gets closer to 0 ohms. This causes more current to flow through the limiting coil and less current through the operating coil, and the needle moves towards empty.
The differential windings give the guage accurate readings despite the voltage fluctuations in the system, in fact, I've heard you can run a 6V guage on 12V with no problems at all. But I would think the resistor is a good thing just to keep the current within design specs.
Hope this helps.
