John's right-the parking lights on one side ro the other can be left on with ignition off and key out to show the car better when parked against a curb on a narrow street-methinks it would run down the battery on a long night, though.
If your left side turn signals work ok, but the right side don't, then the problem is most likely in the turn signal/parking light relay. Use the electrical schematic for your year on Pelican's home page
(here's a link) to track down the circuit path.
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Clay McGuill '66 912
My 912's restoration website, '97 Jeep Cherokee, '70 Ford Bronco
My Bronco's rebuild site