We were there last year, did a night dive off the beach in Grace Bay in front of the Coral Gardens Condos (where Caicos Adventures has a shop). We had a waxing crescent moon, and there were still some glow worms visible - they are most prominent right after the new moon.
Reef in front of coral gardens is a great night dive, we saw an octopus, 2 slipper lobsters, sting ray, hawksbill turtle, some cocooned parrotfish, spiny lobster and a scrawled filefish.
The dive was guided and required advance reservations.