...yes, with the key out and the S and I wire disconnected the I terminal has power.
Ok, that's pretty easy then. Your starter relay is defective. The only possible explanation for power being on the "I" post with only the battery connected is that it's getting power from the battery. And the only time it's supposed to is when it's energized and the starter is spinning.
Sounds like it's time to take it back to see if it's under warranty.
I used the black/yellow wire from the original wiring harness as the link below suggested. If I was to replace this wire what size should I use?
Seems you missed that important bit in the article, and didn't see the mention of it in other places. It clearly says NOT to use your old wire and to replace it with a heavier gauge wire. And that your ammeter would no longer function because of it.
Just another reason to inspect that wire thoroughly throughout it's entire run, or just replace/bypass it to avoid questions. Either method will require some serious work on your part. But that brings us back to checking it to see if you can find an obvious break. Did you do that yet? It's a must on your part.
For this type of alternator, Ford uses either a 6ga or 4ga battery cable sized wire on their cars with this alternator. The size depends on the specific vehicle and is likely related to the overall length.
We sell a kit with 6ga cable and a mega-fuse here:
http://www.wildhorses4x4.com/product/Battery_Charge_Cable_AMG_fused
You can make your own, or just buy a kit and mount it up. The cable runs from the main output stud of the alternator to the Mega-Fuse holder, then on to the battery or starter relay.
If you have room left on your relay's stud on the battery side, you might find it most convenient to mount it there with the other wires. If you're running out of room, it can go literally to the battery terminal on the positive side of the battery. Connect it to the nut and bolt and away you go.
Your old Black w/yellow alternator wire needs to be put away safely. The simplest is to take the end that used to be connected to the alternator and put it over there on the starter relay with all the other wires. If not that way, then you can cut the ring terminal off and cap it, tape it, tuck it away somewhere safe and don't worry about it for awhile.
If you choose the cut-it-off method, you can do it just about anywhere, but farther up the line inside the loom tape might be best.
You will still need the Black wire on the starter relay, but the Black w/yellow wire on the alternator is gone after that. And to get your power back you're going to need to inspect the Black wire at the starter relay. If I keep harping on that, it's because that's what's going to get you back on track. You can't avoid it because that's certainly appearing to be where your problem lies. Don't let it intimidate you into inaction, just yank it's chain until it reveals your answer.
Paul