I think I need some kind of wood filler?

Here's what the back of the headstock neck area looks like after I tried some white glue to fill the open void with.  It looks like it'll take a few more coats of glue to fill it.  Maybe a wood filler will help?

Going to Home Depot to look for the wood filler and maybe get the clearcoat spray.  Darkening the break area like a sunburst style may help hide the discolored area of the damage.