I don't have a direct answer to your question. But when you get the new harness, only undo one connection at a time on the old harness, and place the new harness connection to that spot. Sort of like changing out plug wires on a V8 engine with a distributor. Make sure all connection points are nice clean, shiny metal. Sandpaper will be your friend here, or a small wire brush for hard to get at spots.
And I don't know if I suggested it earlier, but you need to check the voltage output of the alternator, by using a multi-meter across the battery terminals.
The battery may be part of the issue as well at this point, and should be checked, it may not be accepting a charge.

I'm sure you know this, but just in case, and so others might learn as well… Take out the battery while you are doing the cable swap.

The last thing you want to do is have the cable hooked to the positive terminal on the battery and accidentally ground one of those hot leads to the body, either directly or through yourself!

Safety first!

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Jeremy - Aurora, CO
L.O.S.T. #0

Future:
2016 Hydro Blue JK Unlimited Rubicon Hard Rock

Previous:
2012 Flame Red JK Unlimited Rubicon - Sold!
2012 Flame Red JK Unlimited Rubicon - Dealer buyback
2003 Silver KJ Freedom 4x4 - Sold!
32s, Frankenlift, BBars, onboard air, dirt.
KJ EVIC Install

Looking at FSM for 02 shows what the book calls a wiring dia., section 8W-10-7 ,it is information just not quite what I think your looking for.

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02 Sport,Frankenlifted,JBA arms,31/11.50/15 LTB,Aussie locker,204,000m

Yeah,the good old haynes just says be careful,and undo the tape to get at each wire...no real help. Agree this would be an excellent How To subject,have had to redo my cable ends,have looked and wondered about this.Not much room to see,much less get a hand or 2 in there.

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02 Sport,Frankenlifted,JBA arms,31/11.50/15 LTB,Aussie locker,204,000m