Generally all of these types of quirky issues can be traced back to bad grounding. I chased a strange interior lights issue on my '67 years ago, and the culprit was the under dash light housing loose from its frame. The grounding for most, if not all the lights is housing to body contact. The tail lights are the most prone. Need to grab them and grind against the housings every so often to get a good ground. Front turn signal housings are similar. Rust at the housing screws can mess those up too. Also possible your turn signal switch went out. Those are known to go bad. You may have multiple ground issues as well, making it more difficult to isolate. Keep checking everything.
I used to be indecisive. Now I'm not sure. I feel like I am diagonally parked in a parallel universe. 1968 400 convertible (Scarlet) 1976 T/A - 455 LE (No Burt) 1976 T/A New baby, starting full restoration. 1968 350 - 4 speed 'vert - 400 clone (the Beast!) 1968 350 convertible - Wife's car now- 400 clone (Aleutian Blue) (Blue Angel) 2008 Durango - DD 2008 GXP - New one from NH is AWESOME! 2017 Durango Citadel - Modern is nice! HEMI is amazing! 1998 Silverado Z71 - Father-daughter project 1968 400 coupe - R/A clone (Blue Pearl) (sold) 1967 326 convertible - Sold 1980 T/A SE Bandit - Sold
All good advice from 68 topless. The only thing I would add if you have little experience is to always start simple. First check easy things like bulbs and when removing from the sockets check for corrosion inside the sockets because the socket to the metal side of the bulb is part of the grounding circuit. If corroded clean down to bare metal with emery cloth. When testing for electrical faults you need either a multi meter or at least a test light. Clip the black negative side to a known good ground, double check this step. Then take the positive probe and test the socket wire lead while the blinker is on and you should see the power blink on and off, if you do and your bulb is ok then you have a grounding problem And don't forget what 68 topless said, in the front the housing is screwed into the sheet metal for ground and in the rear the sockets get ground from the spring loaded clips that hold the sockets in the tail light housing. after cleaning all your connections put a little electrical dielectric grease to help the connections and to keep them from corroding again.