My Amazon tree boa will not eat .....

[chairman]

My carpet pythons prefer branches that are at least as thick as they are for perching. Otherwise they'll just hang out on top of other objects like cork flats or the top edge of their water bowls.

Your snake may also want a more secure feeling perch. You could try to make sure that some vines are hanging down over a branch, or maybe use something like a finch nest? They appear to make some small bird nests out of coconut shells, they might be easy enough to get a snake out of.

Is the humidity in the tank where it needs to be? Fall/winter can be a drying time.

You'd be surprised how large of a prey item the snake can actually eat. The size of the prey is determined by the thickest part of their body, not their neck. I completely understand what you're saying about the neck size, though, because it doesn't seem like it should stretch as much as it does. They do sell extra small fuzzies that aren't much larger than pinkies. And just a little bit of hair can increase the scent and induce feeding.