Well, the odds of your success will be the product of: (Odds)=(Prior knowledge/skill) x (Craftsman attitude) x (patience) x (Time available). That's the math.
Here's my recommended procedure:
Fill the holes with epoxy, tinting the epoxy with pigment to make it an off-white light tan color. The color of bare maple, not the color of the current amber finish. File the lumps of epoxy flush with the surface. Sand the whole back surface of the headstock down to the bare maple. If you do this right, the filled holes should be nearly invisible against the sanded maple. No need for a veneer cap.
Then repaint the whole back surface with a tinted finish, doing the best you can to match the amber shade of the rest of the neck. This can be the tricky part. It's best to add just a small amount of tint, and build up the shade in several light coats. Trying to match the tinted amber/yellow color in a single coat is hard.