[SunkenCiv]

It went up the nose, typically the left nostril; remember how little kids do art in school (or used to), and poke a hole in one end of a raw egg, carefully scramble the insides, drain ‘em out, and make them into Christmas tree ornaments? That’s kinda the process.

[Zuben Elgenubi]

Here's a photo of some of the embalming tools that I found on Google Image. I'm trying to find the wall mural, located in one of the king's mortuaries, where the process is depicted in the engraving on the wall, where the tools are clearly used.

From the size of the plough tool, I'm going to go out on a limb (no pun intended) and restate the tool went in the mouth, dislodged the jaw and allowed for the evacuation of the contents of the cranium (not through the nasal passage as you suggest).