Not to take awaay from anything Dan has said or did but wanted to add a couple things.
If cost is an issue you could likely find a rebuilt one of these smaller alt at the local autoparts store for about half price. Noticed the one Dan picked is a 60A model but for our little tractors, something a lot smaller, 30-40A, would still be suitable and several times the capacity as the stk model. A gotcha is the drive pulley, you don't want a multi-V belt style.
Last yr I purchased a newer model GM, 3-wire, model at Shucks (same as Kragen or Checkers) for about $60. Was a rebuilt by Auto-lite with lifetime warranty and even had a road hazard policy saying if you were left along side of the road due to the alt failing, they'd pick up the cost for someone to come out and get you back on the road again. Know this is a different situation but does say something about the qlty of the rebuild. I also found the modular connector for the alt I purchased right on the shelf and paid something like $3-$4 for it.
I'm sure there are variations in wiring depending upon age of your tractor so I'm not sure how you would go about connecting the idiot light to have it function properly. An Amp or Volt meter would be a lot easier to address.
Nice conversion Dan. Looks like you did a real decent job.