Despite its name, permanent markers stains are not necessarily permanent. How you approach a permanent marker stain may depend on the affected surface. Fortunately, the permanent marker stain that I faced was on the hard plastic countertop of a toy kitchen. Of course, I first tested with a paper towel and plain water. While the paper towel removed some of the ink, I could quickly tell that this process would be too slow. Next, I progressed to using Simple Green, which was not particularly effective against this type of stain.
In the end, what worked the best was rubbing alcohol. Actually, this is quite obvious in hindsight when considering the alcohol-based white board cleaners that populate many offices. So, I proceeded to scrub away with a paper towel dipped in rubbing alcohol. I managed to remove about 80% of the permanent market stain, but was not making any progress with the remaining 20%. The problem I encountered was that the hard plastic surface was not entirely smooth. My paper towel was no match for the tiny grooves that populated the surface. For my final attempt, I brought out an old toothbrush. Pour a little rubbing alcohol on the stained surface and brushed away. This completely removed the remaining stain from the surface. The toothbrush was able to reach the grooves that was inaccessible to the paper towel.