I've got a sliced up box elder burl that is not stabilized and I've had mixed success at dying it, at least half of the turnings I've started have ended up in the trash. I can tell from cutting open the failures that the dye is soaking in pretty deep, but box elder is very soft and it really needs to be stabilized.
I tried Artisan brand dye that I bought from CSUSA and I don't like it much, the colors are too pale. What I like most is food coloring. Don't buy the small tubes that are located with the baking supplies, get the super concentrated dyes that are on the spice shelves. I like McCormick brand. It is only available in bright primary colors and the dyed turning are pretty intense. I think there was a thread a few months back where someone gave a baker's supply link where it could be purchased in larger containers and more colors.
It soaks in pretty deep, but I don't think it goes nearly deep enough to dye a blank and then turn it into a pen. You can't put a single drop of CA on the turning before dying, the CA area will not take dye and if the wood is pourus enough for the dye to soak in it is pourus enough for the CA to get even deeper, you can't sand it off the surface and get back to raw wood. All CA needs to go on after dying.