Head is pulling left and right

I am surprised setting Head Position Strength, Head Tilt Strength, and Head Scale Strength to zero had no effect. They control ther web came strength over the head movement.

When you placed the stick in the neck did you make it fixed? I just knocked up a quick mockup and that seemed to work?

Yep. Those settings will limit the amount the head will move when you move on camera. Just have a play with them to see if they are getting you closer to what you are after. My guess is 'head position' set to a low number should hold the head in place and still give you some head tilt. You can always move them back to defaults if that isn't giving you the outcome you're after.

If you play with them in your scene, there is a nice little button that will appear (when you hover over it to the left of the setting), that will allow you to push the settings across to your puppet as new defaults. Saves heaps of time.

Good Luck!

Cool puppet!

Here's a few things I would try. Have you tried experimenting with the face settings? They can be found on the right of screen under 'Face'. There you can limit the head position, scale, tilt etc. So if you want to limit movement, that might be your answer?

You could also try raising that fixed tag higher or place a stick in the neck to restrict the bending. You could also play with your head pivot point. In rig mode, select the head layer and then position the pivot point where you want pivoting to happen.

Hope something there works for ya!