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Have an 81 F150 4x4 with a 351M, C6 and dual tanks.
I have a different fuel tank selecter valve than whats shown at the parts store, but i know what i have is factory because the valve has motorcraft stamped on it and also the factory wiring hasnt be altered. I'm having troubles finding this part but this is not what the post is about.
You are right, the O'Reilly part is closer to, if not the, one you need. The one shown at Advance is for the later hard plastic lines, not the rubber ones you should have on the '81.
As for the wire color, can't you look at the switch and find the wire that goes up to the gauge? Or, look at the wires coming from the tanks and you should find them at the switch, so whichever one is left should be the one to the gauge.
There is no switched power for the gauge. It's powered with the other gauges from the cluster printed circuit board. Off the top of my head, I can't remember where that power comes from that goes to the cluster.
All gauges except the ammeter are powered by the Instrument Cluster Voltage Regulator (ICVR) on the printed circuit.
Factory gauges operate at something around 5.5 volts, this is so their readings don't vary as the vehicle's voltage changes during normal operation.
The ICVR looks to be fed from a black/light-green-hash wire from the ignition switch (which has an inline resistor in it so voltage will already be somewhat reduced at the ICVR):
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