You could do it with PVA glue. Polyvinyl Acetate is the standard wood glue, it is easily identified by its colour, yellow.

I recommend Titebond III Ultimate Wood Glue. It has a longer open assembly time, longer shelf life and it initally tacks strongly. It's also water resistant and cleans up with water.

Make sure to use clamp pads when you glue it, you definately don't want round indents on your headstock. Dry clamp as well to see if anything will slide. You've to get it tight with the clamps.

..I was watching my death.
While scouring the web for info, I have decided to use the Titebond which I am going to Lowe's to pick up. After I glue it, I will be putting a small screw to prevent the pieces from sliding when I apply the clamps.
The screw shouldn't be necesarry. One of the benifits of the Titebond III is its strong initial tack. Your break looks like it could be clamped without sliding. The clamping faces are parallel.
Use a softwood such as pine for you clamping blocks. They tend to indent before any damage is done to the hardwood.
..I was watching my death.
I can handle a little expansion. The x4 of gorilla glue is unacceptable. I went to Lowe's today and picked up the Titebond III. Everything I read said this was a good adhesive to use. I'm going to examine the break in more detail to see exactly how to clamp it. I'm putting a lot of time and patience into this and I'm not going to "half ass" it.