Well I've Got Glue in Lowly Places
I get a lot of guitars in my shop that have the dreaded neck or headstock break from being dropped or stepped on. Sometimes, they break into two pieces but often, as shown in the Guild F-20 pictured below, it's not broken all the way through. This is an example of a "good" break (if there is such a thing). Optimally if your guitar has a break, it will run with the grain leaving lots of good gluing surfaces. This guitar's break is deep and is too tight to apply glue the conventional way. To solve this issue, I use medical syringes to inject glue deep into the break before clamping. After the glue cures I'll touch it up, wet sand, and buff out the finish. Lucky for you, you'll never know it was broken.