Yes, regarding the cotton material used to line the glove box.
If by back of the door you mean the garnish moldings around the window openings, the answer is both yes and no. Two grain patterns were used on deluxe coupe dashes, glove box doors, and window garnish moldings. The raised portions of the dash at the top, surrounding the instrument panel, and above the steering column to match the glove box door, the glove box door, and the raised portion of the door window garnish molding along the lower horizontal side were in walnut burl grain and every other area of wood grain was with a straight grain.