Its a fog light indicator your thinking of.
Mine does but it might be a Canada vs US thing. Don't believe there is an RSpec trim in Canada.I only have a foglight indicator on my track model. I don't believe any of the Genesis's come with headlight indicators.
It might be, I have my headlights set on "auto".ManOnFire- Sure that isn't just the parking/marker light icon? My cars asleep for the winter so I can't remember.