As others have said, you'll want to control temperature and humidity and pests. Humidity can be done with either an electric or chemical dehumidifier. Electric requires less maintenance, but requires electricity. You also want to keep it from getting hot. A closed box like that in the Florida sun will be an oven. Can you keep it somewhere that's shaded 100% of the time? Can you provide any kind of artificial cooling/ac?
I keep my gear in a garage, which keeps it somewhat cool. Consistently below 100f. I also installed an electric dehumidifier which keeps it drier. Pest control is already something I am on like stink on gear, so that's also being managed in my garage.
Can you think up a different solution? Maybe constructing a small shed with some insulation, a little bit of proper shingle roofing would allow you more flexibility. You could even run a duct from your central AC to it in a pinch. Just thinking out loud here.
Another option: Don't store it at your house. Some dive shops offer gear storage. You could rent a temp/humidity controlled storage unit. If you get a small closet sized one, they are fairly reasonably priced.
Edit: It occurred to me that the dive shop option is not without risk. I recall at least once reading about a dive shop that stored gear closing. When they closed, nobody got their stored gear back. There's a thread about it on scuba-board somewhere. Crappy situation all around. Storage unit from a chain might be a better option since they're likely to have stuff like insurance and even if they close a location they still need to manage their reputation.
