In Florida it is lawful to have a firearm, loaded or unloaded, in a vehicle as long as it is securely encased and not ready for immediate use, such as in a snapped holster, a closed carrying case, or a glove compartment. Such activities do not require a concealed carry permit. Concealing a firearm in Florida generally means concealed on your person and accessible for immediate use.
Some additional points:
1.) You could conceal a weapon on your person on their property and not be in violation of state law. If they found out you were carrying, they could ask you to leave. If you did not leave at that point, you could be charged with armed trespass. Just because they have a sign up does not mean you are breaking the law.
2.) If any private property owner asks you to leave the property, whether carrying concealed or not, you could be charged with trespass.
3.) What is in your vehicle by lawful means is not the business of any private property owner except the owner of the vehicle, or in such cases where the vehicle is causing a nuisance to a private property owner.
4.) In cases where state firearms law conflicts with county, city, or local mandates, state law will have preemption over those laws. In Florida, it is solely the state that declares and regulates firearms related statutes.
5.) In Florida, firearms and concealed weapons laws are to be interpreted to be favorable towards lawful and peaceful carry. Unless you are clearly in violation of a state statute, no one is going to come after you for going about your business.
6.) Since you are not advertising the contents of your vehicle, it is a moot point.
Cheers,
-Triple T