The Cb500K2 has front run lights in the front turn sigs. The rear sigs do not operate as run lights. (and shouldn't if they are amber)
The front run lights should only illuminate when the lighting switch is on (as well as the Key switch).
The winker relay operates to gate the power on and off to the winkers. If they remain on without the relay, you likely have a grounding issue. The headlight mount ears have (need) a special connection to the greens in the harness inside the headlight bucket.
Cheers,