Operative term is "readily accessible". It has to be securely encased so that it can not be put into immediate use. You will sometimes hear of a "three step rule", but that's entirely true.
From the 790 Chapter fo FSS...( http://www.leg.state.fl.us/STATUTES/...EChapter%20790
(16) "Readily accessible for immediate use" means that a firearm or other weapon is carried on the person or within such close proximity and in such a manner that it can be retrieved and used as easily and quickly as if carried on the person.
(17) "Securely encased" means in a glove compartment, whether or not locked; snapped in a holster; in a gun case, whether or not locked; in a zippered gun case; or in a closed box or container which requires a lid or cover to be opened for access.
(l) A person traveling by private conveyance when the weapon is securely encased or in a public conveyance when the weapon is securely encased and not in the person's manual possession;
790.015 Nonresidents who are United States citizens and hold a concealed weapons license in another state; reciprocity.--
(1) Notwithstanding s. 790.01, a resident of the United States who is a nonresident of Florida may carry a concealed weapon or concealed firearm while in this state if the nonresident:
(a) Is 21 years of age or older; and
(b) Has in his or her immediate possession a valid license to carry a concealed weapon or concealed firearm issued to the nonresident in his or her state of residence.
(2) A nonresident is subject to the same laws and restrictions with respect to carrying a concealed weapon or concealed firearm as a resident of Florida who is so licensed.
(3) If the resident of another state who is the holder of a valid license to carry a concealed weapon or concealed firearm issued in another state establishes legal residence in this state by registering to vote, or making a statement of domicile pursuant to s. 222.17, or filing for homestead tax exemption on property in this state, the license shall remain in effect for 90 days following the date on which the holder of the license establishes legal state residence. This section applies only to nonresident concealed weapon or concealed firearm licenseholders from states that honor Florida concealed weapon or concealed firearm licenses.
Florida doesn't have a State Police. They have the Highway Patrol. Of all things, CCF's are handled by the Agricultural division.