Test what you have first as I said. Take off jumper. Test coil pos terminal for hot. Ignition off, then ignition on. Baseline test. Probably you will find no power in either switch mode
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Answer. In your case, wire from ignition "On" goes directly to coil. I don't know what it really does on your truck.
After coil test at it's pos teminal, next test:
Confirm continuity with mangy coil wire going to IGN Sw.
Confirm it is going to "ON/Run" terminal of Ign Sw.
Confirm "ON" terminal of Ign Sw is cold with switch off and hot when on.
If switch is operating correctly, you can just add a new wire to coil and abandon mangy wire.
Obviously you have a bad wire, bad connection or bad switch, BUT you did say gas gauge comes on. I assume it's wired to same "On" terminal.....SOooooooooooo......