MEK (methyl ethyl ketone) will remove sharpie, and give you a buzz if you use it inside (in other words, use it outside with good ventilation and wear nitrile gloves).
Why would you have MEK? It is used to prep dry bag material or vinyl type stuff for glueing with contact cement. A quart costs about $7 at Lowes/HD IIRC. It also cleans up paddles/plastic kayaks if you want to paint, glue, or otherwise repair them.