Here is a quick and simple way to check if the alternator is working with out any special tools, all you need is a piece of metal that a magnet will stick to, like a simple screw driver.
Pull the hood or sides to make it easy to get to the alternator when it's running, start the tractor, turn on the lights, and touch the screw driver to the back center of the alternator if it "sticks" like to the magnet, even slightly, it's charging.
Start there and report back.