...If I am traveling (and staying in Texas), my gun goes on me. Now, I am only allowed to carry it while in my vehicle and on my property...
I'm (way) over 20, in Texas, but don't have my permit yet in hand. I may have a gun concealed in the car, but it is not going to be on my person for once I step out of the car I would be carrying concealed without a proper permit. Should I get pulled over for any reason, I couldn't get out of the car and be legal. If asked to step out of the car I certainly don't want to be saying, "Officer, let me get this pistol out of my waste-band." And I certainly don't want to be grabbing for it and putting it away as the Officer is approaching.
If a person in Texas doesn't have a permit, I can't see that having a gun on your person in the car is a good idea at all.