This is for Mach headlights, not St170's, but I think they are wired almost the same. Some one can correct me if I'm wrong.
To me, it sounds like the previous owner tried to hook these headlights up as day time running lights. However, all you need to do for that is install a relay in one of the slots in the fuse box with no wiring required. Try unhooking the wire and see if the one headlight no longer turns when the car is started.