These puppets at their base, are rod puppets, mostly with internal rods. What you’re looking at here is the grip and shoulder bar of the fog witch. The grip is the bit that looks like a ray gun. Now, normally, I wouldn’t have the shoulders above the grip, but in her case, her head is even with her shoulders, so it makes sense.
Take a look at the handle. The ergonomics of a control often gets ignored by a lot of puppeteers. Lord knows I did until I had a nasty wrist injury. My occupational therapist at the time rebuilt the handles of several of my puppets and totally changed the way I build puppets. Ideally, you don’t want to have to grip the puppet, because a) the energy that you spend on doing that is tiring and b) the added tension makes your performance less fluid.
This one is called a basic pistol grip, for obvious reasons. See the little nubbin at the top right of the handle? That’s to keep your hand from sliding up the handle. At the base is another nub which cups under the bottom of your hand and adds some stability. You can release your thumb and loosen your fingers with this handle and the puppet will stay in your hand.
The idea is that you want to leave the muscles in your hand free for fine manipulation and use the larger muscles in your arm and shoulder for the lifting. Make sense?
When this is finished, I’ll wrap it with cork tape or leather to control sweating and give a little bit of traction.