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I didn't see your full write-up when I commented last time. The movement you described is typical to stick insects. Maybe it mimics blowing in the wind? It doesn't work if there's no wind though!
I was in South Africa and saw a piece of dried grass moving like a stick insect. If it wasn't for the movement I wouldn't have even known it wasn't dried grass. It looked exactly the same as the dried grass next to it!
I think this is a Swallowtail butterfly caterpillar. A couple of years ago I planted some parsley and eventually I had four caterpillars that looked a lot like this (since it was so long ago I can't quite remember). Those caterpillars also disappeared before they pupated.
I did some research (I have a butterfly book) and figured they must be Swallowtail caterpillars. (I just looked again and more specifically "Black" Swallowtails). The caterpillars eat parsley and the description is "the green and black banded caterpillars are very showy." There are six species of "Black" Swallowtails.
It's a shame none of them made it, the butterfly's are quite stunning!