I think you are on the right track with this.
Went out there and got it all set up so I could stand by the starter solenoid, and start it with a screwdriver.
Got the leads set up... Didn't matter whether I used the case of the alt as the ground, or the battery post itself... The voltage was now 1.24 volts. Not a typo. It was 12.7 before I came in, that last time.
Left it hooked up. Started the engine.... Stayed at 1.24, for a very short while, then started very slowly climbing. Topped out at 11.9volts.
While it was running, I checked the voltage across the battery terminals again. It read 15.63v.
Stopped the engine.
Battery voltage reads 12.36.
"F" to ground reads 12.36 again.
I'll wait a while and then go back out there and check again.
Oh yeah, when I come back in the house, I always disconnect the battery negative cables. So, when I went back out, the cables had been disconnected for a while.