I'm going to have to think about that (what you just wrote) too.
While you were writing that, I was marking up one of the drawings.

To the first question. shouldn't the alternator be hot all the time with battery connected? Yes.
The wire to the alternator will be at the same voltage as the battery.
But, there will be no power flowing in that wire because there is no place for the current to go. The power only flows when there is a lower voltage, idealy ground, zero voltage.

So my first guess (illustrated here) is that the alternator wire was somehow connected to ground. This could have been touching a ground wire, the chassis, or internal to the alternator. Use an ohmeter (or a test light) and see if that wire is grounded.