Inside the white connector, on the battery side, the two green, and one red fusible links are all connected together. I am not sure but I would bet they are crimped together not soldered.
If you are willing to send me the white connector connected to the battery, and the green fusible link connector that plugs into it, I can rebuild it for you as long as it's not melted internally. I can also make up a "repair section" for the cut white wire. See Pic.
You would have to disassemble the green connector on the harness side, insert the white wire through the rubber end cap, push the terminal into the connector, reinstall the rubber cap then solder or crimp the new white wire coming out of the green connector to the harness white wire. You would then be back to OEM with everything new. Figure $50.00 including shipping to rebuild everything and make the repair section. If any of the connectors are melted then I would add a bit for the connectors, but they look like they are OK and the truck DOES run!
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