I don't know what they're offering you, but given what I know of the area they're located in, with lots of very wealthy retirees, they may get a lot of high-end used and vintage pieces out of estates, quite possibly more than the local market can absorb - so
I hope that you can get further information about the dealer, which is the right thing - as well as, of course, thoroughly vetting any watch.
I occasionally go to Florida for estate and down-sizing pickings in some of my other collecting specialties, and while I can sometimes come up with finds and even deals on the sort of pieces that have been sitting or in storage years if not decades, there's also a real problem with older reproductions and fakes that people assume have to be genuine because they've now been around long enough to have acquired a certain provenance as well as the patina of age. Some of the reproducers and forgers themselves retired to Florida, continuing to sell into the retiree communities, including to once-savvy buyers whose critical faculties were declining; there's a whole other problem with collectors (and dealers) who built up a reputation for discernment, but then made "buying mistakes" in their dotage, leaving behind a legacy that is more mixed than might necessarily be assumed.
I don't know if people were passing off high-end forgeries or "franken" versions of watches like Patek Philippes decades ago, but if they were, Naples is one of the places you'd be likely to run across them, maybe even sold as supposedly coming out of the estate of someone prominent. If the watch collecting hobby isn't dealing with the sort of problems and challenges I described above, it likely will be in decades to come.