Crazy stuff like this can be caused by a poor ground somewhere, causing current to back flow through other circuits. I left the ground cable off that was near the parking brake on a mid 70's truck one time and when you turned on the blinkers, the windshield wipers came on?! The good news is that checking grounds is fairly easy compared to finding shorts inside wiring harnesses.
Carl

1952 5-window - return to "as built" condition | 1950 3100 with a 235 and a T-5 transmission