The way I read this, you don't even have to have a CCW permit to keep a gun in your glove box.
527.020 Carrying concealed deadly weapon.
(8) A firearm or other deadly weapon shall not be deemed concealed on or about the person if it is located in a glove compartment, regularly installed in a motor vehicle by its manufacturer, regardless of whether said compartment is locked, unlocked, or does not have a locking mechanism. No person or organization, public or private, shall prohibit a person from keeping a firearm or ammunition, or both, or other deadly weapon in a glove compartment of a vehicle in accordance with the provisions of this subsection. Any attempt by a person or organization, public or private, to violate the provisions of this subsection may be the subject of an action for appropriate relief or for damages in a Circuit Court or District Court of competent jurisdiction.
9/21/06 KY Supreme Court ruled that the console in a vehicle is not the same as the Glove Compartment. They ruled a Glove Compartment is installed in the dash of a vehicle.