I believe this is the Bahamian Curlytail lizard, Leiocephalus carinatus virescens (hopefully I've id'd the correct subspecies), It's fairly common on Grand Bahama. The tail is often held coiled vertically up the back. Unfortunately the only decent photo I got was of one without his tail which somewhat undermines the effect. You can just see his little stump starting to curl upwards.
The use of sacrificial tails by lizards as a means of distracting predators is widespread and well-known. This works due to a weak spot in the tail's skeleton structure and is a good reason to not handle lizards of any species unless necessary - I can remember feeling very guilty after rescuing a tiny gecko from an unsafe household in Singapore only to find it had left its tail in my hand.