SolanaJohn wrote:
Plug in shore power (solar panels still covered)
Solar controller panel indicates 13.7V (no indication that battery is being charged)
Across battery: 12.77V
STOP TMI in your post.
Find out why your shore power charger is not charging the battery. You have an open somewhere, bad charger or miswired wiring.
Your post implies the charger is connected to the solar panels and not the battery. :h Suggest to completely disconnect the panel wires and the solar controller output wires.
Start with the obvious things than need fixing and proceed until it all works.