Glad I saw this as I am having the same issue and I was about to have the fuel sending unit replaced.
Mine will drop to empty after I fill it up and the light flashes. When I get to about 100-150 miles driven on the tank, the next time I start it up it shows full until I fill it up again. It's like it shows empty when full and full when empty lol. Not sure if that was your exact experience, but mine has been doing this for years now.
Do you have any pics of the burned out spot on the board? Trying to know what I'm looking for before I take out the cluster.
Thanks for the info!
This is where it was burned out on the back of my board, at the bottom above the writing.