When the surface is almost smooth continue leveling on the back of the peghead. Use a well-sharpened block plane and take off material in circular motions. Check the flatness frequently by laying on a square. Look for light gaps and mark all sections where no light shines through with a pencil line. By moving the square to different areas you'll get a good impression of where the high spots are. Take them off with circular strokes of the plane. Repeat the procedure until the lines can be drawn almost through.
You can neglect the edges because they are in the area that will be cut off. Measure 1-1/4" (30mm) from both sides on the top of the peghead and mark the approximate peghead contour to get an impression of where the important regions are. Pay attention to keeping a uniform thickness and continue smoothing until you get near the line marking the thickness of the peghead. At this stage you will probably have a hump in the transition area, where the flat part meets the rounded section. Depending on which section is higher, you'll have to remove material from the flat or the round part until the two sections blend into each other smoothly. As a last step use a rectangular scraper and work the entire surface, scraping with the grain until all tool marks have dissapeared.