Good job using the multi meter and book to diagnose your electrical problem.
I am starting to notice that a lot of these old bikes have those rectangular plug in connectors
and the plastic seems to be degrading. The plastic looks dried out, brittle etc.,.
I have see one plug that was near the metal frame of the motorcycle and a 1/16 inch round hole
developed and current had arced through that hole to ground. The contacts inside the rectangular plug connector may not be isolated from each other because of the degrade plastic.
Just something to be looking at on all of these older motorcycles.
BTW when the battery is charging it should get higher than 13.8 volts
See a 12 volt battery has 6 cells and each one is at least 2.1 volts. (lets not quibble),
So 2.1 volts (per cell) x 6=12.6 volts- So a 12 volt battery is more than 12 volts, and can be as high as 13.8 volts when
the motorcycle is NOT running. Then when it is running and above 1500 rpm it could be charging at around 15-17 volts.
On a Roadstar Adventure.