I was burning a cone incense and left it on the sink, and this stain won't come off. I tried baking soda, water, vinegar, hydrogen peroxide. I tried letting them sit for multiple interations, and it made no difference.
Just chiming g in on the non polar stuff. You could try hand sanitizer too. I had some stains from dye that would not come out of my tub and hand sanitizer did the trick!