I disagree. Farmers and ranchers keep long guns in their trucks. Police officers leave shotties and ARs in their cruisers. If you enter a federal building or a school then you BETTER take that thing off your hip and leave it in the car. What I'm saying is - it happens all the time. As long as you have a hard top and the doors locked I think your liability is nill (follow applicable state laws of course...). A tuffy box under the seat may make some people feel better, but a criminal could deal with that in a few seconds with a crowbar. If you have a soft top (or no top) and the "strong" box is there to keep kids out or due to state law it might make sense. From a liability perspective I think the glove box works just as well...either can be broken in to with minimal effort, but they both "lock."
The mere presence of a tuffy says "Hey, criminals, I keep a gun under the seat or in the center console." My glove box looks pretty non-descript and probably makes me less of a target in the first place. Not that I often leave a gun in the car, but there ARE times when it is a must. Ever go to the post office?
The only truly safe place for a gun is on your hip! You know if you are going to the fed bldg/school before you leave the house, so, leave it at home, or put it in the provided safes at the entrance. If you are that concerned about traveling with a weapon in your vehicle, then don't bring one. Simple as that.
Most farmers and ranchers I know are on their private property and these CCW laws do not apply to them. And most farmers and ranchers I know utilize long guns of some sort. For Jeepers and their daily drivers, this is another issue and the one the OP is asking about.
Yes, cops carry their weapons in their mounted steel weapons' carriers. These are made specifically for a shotty, or shorty. They are locked and secured. Most departments I know of require the officer/deputy to remove their guns while parked at home while 'off-duty'. 'Most'
The OP asked what to do with their concealed carry weapon? CARRY IT! or don't if you are not secure with it. Practice, practice, practice from drawing from your hip/cross-draw/chest rig or however you conceal your weapon. For the one and only time you need to draw your weapon under stress, you may lose your chance if the attacker is faster than you, or ready for action.
Don't be a sheep, but a sheep dog! For the wolves are out there.