I have used with great success:

1. Acra glass in both varieties

2. Titebond wood glue (wood needs to be clean)

3. Good ol' fashion Elmer's wood glue here again the object is clean.

Drilling this crack might only further weaken the stock, but it will stop that crack from advancing along THAT grain line, most likely if left untreated or not treated properly it will find another, and just continue. I would not drill it...

Double guns and English Setters