Both rear turn signal lights flash

Got a weird one for ya. I'm a tech with 30 years experience and I can't figure this one out! No matter how good ya are, sometimes you get stumped! Truck is my personal ''winter beater'' and tow vehicle for my drag car. When the R or L turn signals are activated, BOTH the rear lights flash. Front is fine. Headlighs on or off makes no difference. Using an unpowered 12V test light with the firewall harness plug disconnected I checked power feed from the column switch. Both sides work as they should, so the problem is not in the turn signal switch. Problem SHOULD be a short in the wiring harness between the firewall connector and rear lights, but it is NOT! Unplugged the connector at the rear of truck and used a test light. This cut out of the circuit ALL rear lights and tralier light connector. Power was fed to both sides, the Yellow and Dk Green wires. i.e. both sides flash at the same time. Used a DVOM set on ''continuity'' to check wiring harness between firewall and rear connector. There is NO SHORT in the wires. Checked and cleaned the rear frame ground while back there. Additionally, when I hit the brakes the signals cease to flash. Hazard flashers work and I checked both relays. Both click and I can feel them cycle when I touch 'em. Everything else, brake lights, park lights, headlights, all bulbs, etc are fine. I haven't checked the brake switch and circuit yet, but looking at wiring diagrams I can see no way where power could feed back into the rear wiring harness and cause this problem, unless coming thru the column switch, which checked out OK. The problem was intermittent for awhile, usually when wet or raining, but now is permanent. Anyone got any ideas here? What am I missing? My problem is the same as one ride, except it only happens when the right signal is on. Left is fine. Symptoms are otherwise exactly as he states. My truck does not have a trailer plug. Any solutions yet?