That is exactly how my panther is and has been since the day i got him. I took him out of the box he was shipped in and tried to pout him in his cage but instead he climbed on my arm. He sill comes to the screen of the cage and sits there waiting for me to take him out and if i put my hand in...
Do you have zip ties in your cage? If you do make sure they're all cut as close to the lock as possible and make sure the cut isn't angled to prevent them catching on your chameleons skin.
I don't know the best way to go about opening their mouth. When I took Skittles to the vet the vet held him kinda with her 4 fingers lightly over his back and he was actually sitting on my hand and wouldn't leave me. She used a popsicle stick to help open his mouth and keep it open. I don't know...
You can use some sort of plastic to cover the sides of the screen cage. I've also heard that people use shower curtain or fish tank backgrounds. You could also think about making a drainage system. also try to spray from the top of the cage so the water won't hit the walls as much maybe.
We have quite a few pets and one of them is a Quaker parrot. We built this bird stand for him to come out of his cage and play but I think we will actually be getting rid of the bird because they require so much attention and recently we haven't been able to give him that. Anyways I was thinking...
I got a new battery and it seems to work fine now. Earlier today i checked it and the temp said 103! I was thinking theres no way so i grabbed my temperature gun and that read 83. Anyways the low battery was making all crazy im assuming and it seems fine now.