Obviously a connection is being stressed, or a wire is failing somewhere, that opens up when you turn the steering.
Check the earth connections, as these will be common to both functions.
Unfortunately when the lights and gauges move with the steering, the loom is expected to flex with it. As looms become more elaborate, with more wires, this can be problematic.
I had a similar problem with my Elefant, causing the tail light to fail. That was one of the wires from the ignition switch, which had to flex too far on right lock. It failed adjacent to a clip that held the wiring to the frame.
After I repaired the failed wire I left the loom out of the clip, and have had no further problem. Often there will be a primary power wire from the ignition switch which could affect both headlight and park light functions.
Sorry I can't be more specific than that, as I haven't encountered this problem on that exact model.
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