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It is easy, get enough spools of stranded, oil/gas resistant wire and since it is a single conductor the voltage of the wire insulator will be high, 600V, but stranded.
Set the rolls to unroll the wire at your convenience.
Using wire markers 0-9, A -Z, ID each of the wires as you pull them in to the screwed up harness and use a piece of wire to tie them in place temporarily.
With the new wires in place next to the harness that will be redone, match the new wires to the older wires, twist them together loosely to show which new wire will replace the old wire.
All set strip and make the joints and use heat shrink to seal each, one at a time. Leave the unused wire your replacing as a guide to know what is done, being done, still to do.
When all are soldered and checked remove the unwanted mess.
Now with the new mess, clean it up, remember wires can be bent, if too long cut and re-solder.
In time you will have it done, but as you go keep a log, record all of this, what wire to what colour.
The idea of having spools of new wire helps keep the mess to a minimum, DO NOT KINK THE WIRES.
If you are not good at soldering take some wire and make twisted joints and practise, make a lot of joint pieces and try soldering all of them, use resin core solder, get a small amount of resin paste and play, the longer you play the more expert you will be.
Often resin paste helps when 3 or more wires are attached as a joint , the paste cleans and creates a much easier transition from soild to liquid as the solder melts.
Experiment with solder configurations 50/50. 60/40 etc as the amount of lead and tin changes the3 melting point.
The soldered connection must be done with a hot tip, the ideal situation is to heat the copper wires and then place the solder wire onto the copper and then the solder will flow onto and through out the joint, never place hot solder on a cold wire, a cold joint will result and not work.
Look for the joint to be copper, shiny solder, then a duller solder when it cools. This is a time to practice, because practice makes perfect and you want to be perfect in this.