Aaaaaand the first stain is on the body. Don't think it needs any black on it from here. I think I'll gently sand it, do another light coat, and leave it at that.
Also got 99% of the tape off the neck. The glue had hardened it in places. I got a couple of bleeds and runs that I'm not sure how to fix beyond just sanding them until they're gone.
In future, what I'd do is to mask 3 layers so that none of the tape that hardens is in contact with the neck, only with the un-hardened tape below it.
Edit: It's tempting to try a mild burst with the black japan though...