People in the thread are telling you to use wood glue, and while this specific location would probably be fine, you should know that the rest of your guitar was assembled using hide glue for a very good reason.
Wood glue is very pliable and plastic in texture which is great for things like tables and chairs that are frequently being flexed as loads are applied and removed. The trade off is that the glue joints absorb vibration, which is VERY bad for an instrument.
Hide glue is more rigid and does less dampening. For this split on the headstock there won't be a noticeable impact from using wood glue, but didn't use it on other parts of the guitar.
Fingerprint unlock would be even easier.