Rick is correct on the "floating" ground.
Some cars used the same system years ago, the 2 wire ungrounded marker light was connected to both the run & turn circuits.
When the turn signal was off, the marker was grounded thru the turn filament, so the running light was on. When the turn signal is on, the marker bulb it "hot" on both sides during each blink, causing the marker bulb to blink off, then between blinks, the marker bulb sees ground, so it blinks on. You can confirm it is wired this way by watching the marker & turn signal alternate blinks. I just had this issue when I changed my tail lights to led. With the running lights on, power backfeeds to the turn filament, so it only flickers when signal is on, due to constant feed thru the marker bulb. I will just disconnect the wire to the turn signal & ground it. This makes the marker only a marker, but that is ok, you can see the curved taillights from the side as well...
Edit to show confirmation of success...
https://photos.app.goo.gl/17qKkwLnMv5r7tyv9