Linseed Oil Didn't Work
Well. The boiled linseed oil didn't work. At the end of the day it seems that there is nothing for it to penetrate into. That black polymer or whatever plastic material the layer on the top of the headstock is made of has no "pores" or space molecularly for the linseed oil to penetrate into. The oil just sits on the surface and cures. It created a slick looking sticky surface which clouded upon touch after curing. It peeled off with even moderately light rubbing to try to remove the dust and particles which would gather on its sticky surface. So, after rubbing it all off, the black plastic material was in it's same discolored faded condition as before the linseed oil treatment.
Thanks for the idea, though. If you don't try it, then you don't know. Well, this one was tried. Bummer.