I chased a problem almost identical to this. I rewired the rear tail lights, replaced the turn and hazard flashers, and even tried 2 different turn switches in the column. For me it was intermittent, only happened when I had my parking lights on. What I failed to check was the front fender lights wiring. I found the wire to the drivers side fender side marker was randomly cutting out (crusty wire does that). I replaced that socket and the first 6 inches of wire where it was cracked up wiring and it solved my problem.
Moral of story is you have to check every bulb socket make sure you are getting connectivity, if it disconnects the system is designed to make the bulb go solid in the dash to indicate that a bulb is iout.
