The "Sharpie" brand markers seem to be alcohol-soluble, but if the ink has been there for a long time it may have diffused into the finish and be more or less impossible to remove completely. The good news is that when you find a solvent that doesn't touch the ink, you can look for a "repair" finish that doesn't mix with that solvent, to paint over it without bleed-through. This is the principle behind using shellac (alcohol-soluble) to seal resin pockets and knots in pine (turpentine-soluble, like varnish). In your case, of course, you probably want something of appropriate color and gloss that is alcohol-resistant. (Model-airplane dope is a likely candidate, because the engine fuels are alcohol-based; for flat white, consider White-Out or similar correction fluid.)