In Cayman, aint nobody gettin' in the water without a DM. Not during the day, a for sure not at night.
More likely a "dusk dive" so the pre-dive thrashing around on the boat has a bit of illumination.
The briefing will be about "how to night dive" with an explanation that the ladder of the boat being marked with a flashing strobe. (This works pretty well until my buddy, that doofus from Chicago, jumps in with his newly acquired strobe going blink-blink-balink tied to his tank so everybody starts swimming after him at the end of the dive thinking he's the ladder. I seen it.)
Czyalume Glow Sticks are equally useless and they pollute the island with trash. They are a marketing gimmick at dive shops and serve no useful purpose. My LDS sells a lot of them to the girls at the local
"Vegas Style Dancers Club" and they smear the glow juice all over themselves so the patrons can better see them in the dimply lit club... I guess- I wouldn't know. (But it just won't come out of my Polo Shirts) Glow sticks are absolutely a waste, some dive ops require them- it adds to their profits. Buy a battery powered version
http://www.diversdiscount.com/resources/frameset-search.asp and be done with it.
The other excellent use for glow sticks is to attach them to the ceiling fan, turn off the lights and try and remember the sixties. If you can remember the sixties, this probably won't work for you, however.
Some think that they can "mark" their dive buddy with them. They are sure to stand out from the other twelve divers with the glow sticks. The red ones disappear visually, all the others look to be the same color. That doesn't work, either.
Go to Cayman, sign up for a "night dive". It will be the calmest easiest no-brainer night dive you'll ever have. It will be fun, no matter what!
Subsequent dives in other locations with more training will open up a whole new world to you. Turn out the lights and look at
http://www.cocoviewresort.com/frontyard.html I do it at 8 and 11 p.m. whenever I'm there.