I have always taken the pistol locked in a gun vault pistol box to the counter. Told them I want to declare a personal firearm. I then open the box and put the whatever paperwork inside. I lock the box and use the cable yo secure to the interior frame of my luggage. Some airports have me take the gun to the screening area. Indy does not. I think they have a form I give TSA when going to the gate. Been awhile since I have flown. TSA at Indy asks me for the combination to check. Other airports have me stay with the bag and pre screen. Never a problem.
Got it. I use key lock(s), but I've never been asked to open the case by the TSA or gate agent. I just stuff the paperwork in the case while its still in my checked bad so it's doubtful anyone even sees the case. I did have a gate agent in JAX tell me NOT to unlock the case. I asked her how I was supposed to put the paperwork inside without opening it. She thought about it and told me just to put it in my suitcase. By that time I'd already put it inside the pelican and re-locked it. I wish everyone was on the same sheet of music...