I greatly appreciate the responses. I don't know what I'd do without your help.
George, as for the questions you asked, up to this point, the fuel gauge dances only when the car is in motion. It is typically erratic when turning corners or hitting bumps.......but sometimes dances during steady driving on a smooth roadway. I have wondered about a loose connection, and I hope that's the cause of the problem. In researching the problem on the "ShopForum", I read where a bad batch of gas can cause deposits on the wires within the "sender"........and careful and delicate cleaning can solve the problem. I'm just not quite sure what solvent to use for the cleaning.