They are an anemone dwelling species. However that particular one is not seen in the hobby as far as I'm aware.. although a very close relative, Periclimenes brevicarpalis, is fairly common.
Another species, Ancylomenes venustus is a very active and similar looking species.. infact almost identical besides some missing blue bands Periclimenes amethysteus has, while be a little more limber and skinny.
Movement pattern wise I have no clue as like I said I've never seen them in the hobby.. however Ancylomenes venustus has a very entertaining movement pattern that makes it one of my favorite anemone inhabiting species.
All these species are harmless scavengers that eat detrius and other foods.