Fuel Gauge Pegged

The needle only pegs in one position - way above full. It never pegs anywhere else. Except of course when the ignition is off, which it's supposed to do.

Update to the update: the gauge pegged way above full again. I discovered that the connector by the taillight didn't fix the problem. I finally gave the wire going from the taillight area to the fuel sending unit a few gently tugs under the chassis, and that fixed the problem again.

So I guess once the weather turns dry (sometime around June) I'll be pulling the tank again and inspecting the sending unit. It may just need a little solder or crimping or something.

Sounds like you fixed it by cleaning the various connections.
I would suggest to you and everyone that is (body part) deep in older cars to do a systematic wiring cleaning. Everywhere the wire touches ground, remove it and clean to bare metal and reattach tightly. Everywhere there is a connector, disconnect and clean. The fuse block needs to be clean and shiny front and back.
GM makes a contact cleaner that is expensive but great for this type of work. Radio Shack has a cheaper version.
The hard part is to avoid creating more problems due to age and brittleness.
Take your time and carefully clean each and every terminal, connection and ground. Electric Karma will be yours!

Well said

Or do as I am doing, and build a complete new wiring loom including lampholders, terminals and connectors