I don't know where you have been diving in Connecticut, but if you've been diving in low visibility, you've already had some good preparation for diving at night. And night diving in the tropics is about as easy as night diving can get, because your lights will carry through the water easily and you will just about always be able to see the bottom. Disorientation was a big issue for me in my first night dives -- If I got very far off the bottom, I couldn't see it, and since there's no gradient for light from the surface to the bottom, it's easy to lose track of which way is up. (Or at least for me, it is.) This is not really an issue in the tropics.
I don't think you need a class in night diving to do it. My night dive in my AOW class didn't do a whole lot more than let me have the experience of being in the water at night with an instructor as my buddy.
People have already brought up good issues. You need to keep track of your buddy, and it can be difficult to recognize YOUR buddy if there are multiple divers on the site. That's where some kind of recognition signal, like a colored glowstick, can be useful. You need some kind of light discipline, because light signals are part of night diving, and if your light is waving wildly around, it makes its usefulness as an emergency signal very low. You definitely need a backup light, and you need to check that it's working before you begin the dive.
For tropical diving, the LED backup lights make wonderful primary lights. The
UK SL4 eLED is a very bright light with a focused beam, which is good for looking at critters but also for signalling, and is reasonably inexpensive.
Remember, always evaluate your own level of comfort and fitness for doing any sort of dive. There is no stigma attached to hiring a DM to guide your first night dive -- You may see things you would otherwise have missed!