If one tail light works you probably have a problem at the rear since they are directly connected. Probably a bad connection at the rear electrical panel, very often just a corroded terminal or wire. Had a bunch of those in my 4104.
Again, I'm assuming Eagles have rear panels.
Turns and brakes are on a different circuit.
I'm eventually going to put my dash lights on a separate circuit, I'm pretty tired of this problem!
Again, older GMs have tail lights, dash and markers together.