This recently happened to me. My issue was that while testing the circuit to determine running vs turning lights, I shorted something and blew my tail light fuse. For some reason I don't fully understand, this meant I had a brake light but no tail, running, or turning lights. I was still testing 2V on the turn signal circuits, not enough to make them flash. When I found the blown fuse for the tail light, it all went back to normal.
Your circuit sounds different, but could be a similar issue. I am sure you've checked for blown fuses though?