Have you got it untaped as well? That would be good for looking at splices and other hidden gremlins.
If the battery seemed to be charging at all, and the ammeter showing a charge, then it seems your charging system is ok.
I wonder then, if one of the main splices is deteriorating inside. There are one or two main junction points buried in the tape under the dash. Sometimes black, sometimes another color, but basically just a block of molded plastic with several wires leading into and out of it.
If any of those are broken, that might lead to what you're describing.
Hard to imagine that though, from the general quality and longevity of the factory splices. They're usually fantastically done.
Then again, the more common culprits would be two things. One is the individual components themselves getting old and rusty or weak, and creating too much resistance internally.
And two, and just as common on Broncos, is the deteriorating ground wire/connection issue. Some break, some corrode, some just get removed during servicing and fixing during an EB's lifetime, and too many rely on a good connection between the body panels.
Is yours getting kind of rusty? Even if not through and through, then maybe at the seams and such? Especially between the inner fenders, core support, wheel wells and firewall?
I could see too much reliance on physical contact being a grounding problem on a lot of EB's.
Of course, the wire that melted on yours is only used during start anyway, so that one thing seems more likely due to a faulty component or wire.
It's the drop in voltage that seems likely to be a ground issue.
Paul
