I think that's what the yesterday's tractors thread was referring to, the 1 and 2 next to the R and F means that the aluminum case could contain either an internally regulated or externally regulated alternator. You might be able to tell the difference by the layout of the spade connectors that point up in the picture, whether they are inline or what. or take the back cover off and get us a picture of the insides.
Regardless if it's internally or externally regulated, if the three terminals were connected and the voltage did not rise above 13V with the engine running, and revved once or twice, then the alternator itself is not functioning. If it has an internal voltage regulator, there's probably a tab that you can ground to the case with a small screwdriver that will bypass the voltage regulator and put the alternator in full output (D hole in the photo in the link), if that works then you just need a new voltage regulator, and if it doesn't work, you probably just need new brushes and regulator. That alt looks clean enough and genuine, that I'd repair rather than replace. But diagnose first.
I'll run an alternator on a bench hooked to a battery and spun with a 3/8" drill or screwgun, 1/2" drills usually won't go fast enough.