Your first diagram shows, I believe, the "one wire" alternator. It appears that you have the classic "3 wire" Delco 10SI, but check the numbers to be sure you actually have a alternator with an internal regulator.
So, you can't wire your alternator according to your first diagram. The 3 wire alternator is arguably superior anyway, and if wired correctly, works great. Hooking up a 3 wire alternator can be confusing because you can choose different points to connect to and it's a matter of personal choice.
The simplest way to wire a 3 wire alternator is to loop a short wire from the #2 terminal right to the battery output post as shown in the Vintage Garage image you posted. However, it is considered better if you can connect terminal #2 of the alternator closer to where all your accessories and components draw power. In your case, it's probably on the "load" side of the ammeter. Original Jeeps served out most of the power for the gauges and lights from that load side of the ammeter.
The #1 terminal of the alternator needs to be wired to the "ON" terminal of your ignition switch. This basically turns the alternator "ON" and allows it to charge. More importantly, it removes battery power to the alternator (turns it "off") when you turn the Jeep off, and prevents the battery from getting run down.
The "BAT" terminal of the alternator could be run with a 10 gauge wire to the "BAT" side of your ammeter. Some folks don't like passing another 10 gauge power wire through the firewall, so you could simply run it directly to your positive battery cable clamp. (You might want to get a new positive battery cable with an extra lead for this purpose).
I'd be nervous having my ammeter hanging out of the dash. That's a BIG short just waiting to happen if you hit a bump, or your foot. Instant melted cable, smoke, fire.
By the way, sometimes folks who've switched to 12V just get rid of the ammeter and put in a Voltmeter instead. Something to think about.
If you ordered a stock harness, you won't get a fuse panel, or a ballast resistor setup; a few nit picky things about a 12V conversion that you should make sure you get right. Check out your coil to see if it's external or internal resistor.
But anyway, you can modify a stock harness to make it work for you without much trouble at all.
Good luck!
Dave