Using 18 percent gray toned paper is an excellent choice for illustrating the human skull. Also using both white conte' crayon for the application of lights, and charcoal for darks is often the best method. I see you have also tried a tan colored toned paper, we used to make use of brown paper grocery bags until they began to water proof them with varnish.
I always try to imagine that basic form of the skull is a box, that way it is easier to model it in tonality after establishing the light source. Remember that shadows are the darkest darks while shade is a much wider spectrum of tonality. Save the brightest white for highlight and don't disregard adding a full range of tones to the background to sharpen contours.
In detail it is interesting to note that the skull has only one moving part, the jaw. It's hinge point is just below and inside the ear. Pay particular attention to the zygomatic arch as its proportions vary from specimen to specimen depending on the original models genetic characteristics.
Lastly, practice, practice, practice. Oh, and get a real skull to draw, not a plastic one. An anthropology department should have tons of them lying around in a closet somewhere? Is Dr. Herbert Phillips still teaching in the Anthropology Department at CAL?
...just some of my CO2