Steve (rvrtrash) may be able to step you through a test with a volt ohmmeter. You need small pins that you can stick into the individual wires at the connector for the turn signal switch. You can see the power side that goes towards the turn signal switch and see if it comes back down to go to the taillight harness.
The brake lights, the emergency flasher, and the turn signal flasher all go through the turn signal switch which is a combination turn signal and emergency flasher component.
My bet is it is time for a new turn signal switch. Very common for them to fail with the 6 taillights power needed to flow through them. Also seems like the new replacement switches are not very durable either. One fix help is to go to LED lights. They draw less current and put less stress on the contacts in the turn signal switch.
By the way, I replaced my turn signal switch in 1989 and then again about 3 years ago.... I have LED lights now.
Steve is looking into whether their is a heavy duty alternative to these switches. Thunderbirds used lots of taillights.
Rob