There is no absolute, explicit "right" to total privacy. There are many arguments that there is a privacy right, an inherent one, to which all persons are entitled as a human right. There is an argument that it is covered by the 4th and 9th Amendments of the US Constitution. There is a right to privacy in the Florida Constitution that, like most others, pertains to government intrusion.
Of course, even the 4th Amendment right to be "secure" in your person, home, papers and effects can be breached by warrant supported by probable cause but, again, that applies to government intrusion, not your neighbor's security cam.
There is a civil, common law right to "seclusion" in an area reasonably expected to be "private." Intrusion into seclusion is a cause of action but there must be damages, where the breach caused you some emotional distress, embarrassment, job loss, reputation damage, standing in the community issues, etc.
Gated communities offer protection from outsiders but ironically, they often offer less protection from neighbors because they often prohibit privacy fences. Do you have a privacy fence? Does your neighbor's camera peer over that fence? Does your rules and bylaws speak to this issue directly? Often, gated community HOAs are quasi governmental in nature and have broad powers you agreed to abide by.
I suggest you voice your concerns to the neighbor directly. Document your communications with them. Complain to your HOA and document. Perhaps suggest adding this issue to the bylaws and address the privacy concerns. Use the Florida constitution as a grounds for adding an amendment to your bylaws. If you feel some private activity is being hindered, document that. If you feel you have been damaged emotionally or financially, or in reputation, document that. If you feel you have enough to file suit, speak to an attorney who works on a contingency basis. If your case interests them, you may just have something.
A more passive approach may be to simply put up something close to your property line that blocks the camera's view: a flag, or an umbrella, for instance. That is, after you ask your neighbor to twist is away from pointing into your yard.