Your turns on the right (passengers side) need a ground. Since they have lost the original ground, they are "seeing" the bulb filaments as ground. Not a good ground, but better than no ground at all.
For any 12V citrcuit to work, it needs B+ (positive 12 volts), an electrical device of some kind to do some kind of "work" for you (in this case, make a light bulb light up), and a path to ground to complete the circuit. A length of wire has some resistance, the filament of a big light like a headlight has more resistance.
If your turns cannot find a path to ground when you energize them they will seek out any resistance they can find and call it ground. If the aquired ground is a weak resistance, your turns may glow a little but not really function. But if they can find a ground through a big resistance like the headlight filaments, they will likely work reasonable well. When you apply B+ to the headlights, the turns can no longer find a path through the headlight filaments, so they stop working because they have lost the "path to ground" needed to complete the circuit. In this case, a flase path to ground, but a ground of sorts none the less.
As a genreal rule, whenever electrics are acting really weird, you are pretty safe in starting out looking at the ground situation for the suspect circuit.
Welcome and good luck, Robert
1988 Black Spider Veloce with a few weird elecrical problems of it's own.
Last edited by vf31rhill; 11-18-2009 at 04:39 PM.