Too lazy to read the above posts so I'll just answer the OP's question:
In FL if you are 18 with no concealed weapons permit, you are authorized to keep a loaded firearm in your glove box, locked or unlocked. Other authorized locations are any place where it can be "securely encased", which is defined as basically anything with a lid, a door, a zipper, etc...something you would have to open to get to. As said, it does not have to be LOCKED in said compartment. Even with my CCW permit, I often carry in the glove box because it's easier for me to reach over and open the glove box and grab it if I need to, rather than take off my seat belt and wiggle around to reach it. You do not need to notify a LEO if stopped, however if they ask, it would be wise to answer honestly. I have gotten out of citations because I notified a LEO immediately upon the stop that I was carrying (I hate doing this as a Libertarian, but I also hate paying tickets or making a stop awkward if it's discovered I have one and didn't notify). LEO's generally appreciate it, as it will generally help put your mind at ease that "Hey, I'm dealing with a law abiding citizen."
When I was in the academy during the traffic stop portion, we had a Sergeant from the local sheriff's office traffic unit come out as an instructor. His logic, whether you agree with it or not, is that if he stops someone and they notify him that they have a firearm, they get a warning. "You save my life, I save you money." A lot of cops feel that way, as most cops are generally pro-2A.
Got pulled over February, 2012 by Lake County S.O. here in FL on my way to my Nat. Guard drill on a Friday night. I was in the middle of nowhere on a country road, didn't realize I was going 80, and didn't know the speed limit was only 55. I honestly thought it was 60 or 65, and thought I was going about 65 70. Just listening to some tunes and thinking about how there is a million other things I'd rather be doing on a Friday night. I come around a long bend, and pass a deputy on this two lane road going the opposite direction. It's still dusk, and I see his brake lights light up my mirror, and he goes off into the dirt, flips a 180 to come back in my direction now...this is when I say "Oh ****" and look at my speedometer and it said 82 or something. I immediately pull over because I know where this is heading and get out my license and registration. He obviously flips on his lights and pulls up behind me, and I'm just wondering how I'm going to pay this ticket.
Deputy: Hey man, I just pulled 2 of your buddies over (I'm in my uniform)...how many more of you am I gonna pull over tonight?
He said it in a real joking manner and I couldn't help but laugh. I apologized, told him I wasn't really paying attention to my speed, and he notified me that I was going 80 in a 55...
Needless to say I thought I was screwed...I told him as I handed him my license and registration that I had a gun in my glove box and he said "I don't care, fine with me"...got a written warning. Like a boss.
Last war story here...got pulled over by FHP 2 weeks ago. Dialogue went like this:
Trooper: I need to see your license and registration please, you have a headlight out.
Me: Okay but before I go reaching for anything I want to let you know---
Trooper: You have a firearm on you.
Me: Yes.
Trooper: Okay not a problem bud, go ahead and hand it to me. Where's it at?
Me: My right hip.
Trooper: Ok yep just hand it to me.
Me: ...you want me to just hand it to you?
Trooper: Yep, go ahead.
Me: You don't want me to get out and you can take it off of me?
Trooper: Nope, go ahead and just hand it to me.
Me: Uhh, okay. *Awkwardly and slowly reaches for Glock 27 on right hip with left hand, hands him Glock 27 in the holster*
Trooper examines weapon with his flashlight.
Trooper: Oh very nice, a Glock is a fine weapon...I'll be right back.
Brings me back a written warning, handed me back my weapon in the exact same condition I had handed it to him in...meaning 9 in the mag and 1 in the chamber :] I thanked him for letting me know that my headlight was out, and I was on my way. At first he was very stand-offish as any LEO should be on a traffic stop, and after I notified him that I had a firearm he almost seemed relieved and became quite a friendly guy.