It's not 'normal' for rosewood (or ebony) boards to have any finish on them at all. Some lemon oil from time to time to keep them from drying out, but normally that's it. That's not to say you can't put a finish on a rosewood board. Rickenbacker famously gloss their rosewood boards, but it's not necessary. Maple boards need something on them to stop them oxidising and turning grey with use and with acidic oil and sweat from your fingers, but rosewood and ebony don't suffer in the same way. They can still get dirty, so should be cleaned from time to time - scraping for heavy build ups followed by naptha or lemon oil to get the dirt off. Some people here like to use a clear wax to feed a rosewood board and give it a smoother feel. It's all personal preference.

I'd see if something like naptha (liquid lighter fuel) will clean off the DT on the board. Don't forget to mask off the rest off the neck as you don't want to ruin its finish. If naptha doesn't do it, I'm not quite sure what will. You'll need to let it soak in a bit then rub teh area with a clean cloth - though as it quickly evaporates you'll need to keep adding a bit more. It's very flammable stuff, so don't use it near a flame and best done outside in the shade.

Any liquid (like lemon oil) or wax will make the wood appear darker, so if there's any of the DT remaining, you could lemon oil the board, or use the plain DT wax that PBG sell on the board, which should get the board looking as dark as any areas with some DT finish still on.