Pithing: insert the tip of a sharp knife up through the open mouth into the brain. And you are trying for a quick death so could jiggle the knife around the be sure... i have done this with chickens before, not as the main killing but immediately after cutting their jugulars when butchering because I read that it can help loosen their feathers, they definitely died faster than when I just cut their throats... it didnt seem to affect whether the feather pulled out faster or not, but i was probably hiting the wrong spot in the brain, and it was older roosters, so i only did it a few times. (Most of the time i dont pluck anyway, I skin.)
Doing it like this would give you a fully intact bird though. I know theres better instructions either on this site or just googling it on how to kill birds this way.
Edit to add found this:
https://www.backyardchickens.com/threads/butchering-using-a-knife-to-the-brain.1273368/
And a quick search brings up lots of good stuff theres even videos on youtube
Beautiful lizard by the way