The oil, sorry. The Sharpie will soak in immediately but the oil takes a little bit, at least a few hours or so. I've used Sharpie several times, especially for touch up. I believe it mighta been @YinTx, but I usually use Fiebings dye as edge dressing and then just slick as usual. I've recently started using glycerine saddle soap on a damp edge as well with pretty good effect, whether rubbing with canvas or a slicker.
I don't even own mink oil...