I used to keep my TDL and CHL in a separate small leather folding ID holder. It flips open and will display both IDs. I used to keep this ID holder in my shirt pocket so that, if asked for ID, the officer could see my hands at all time while producing it, and my hands never went anywhere near my gun. This system was put to the test only once (I've only ever been stopped once in the 5 years since I got here), and it worked quite well for me.
The officer came to my window, which by the time he got there my window was down and my hands were on the wheel. Because I was coming from just having had a chiropractor's appointment, I just had gym shorts, pocket t-shirt, and sandals on, and my gun, along with the rest of my usual pocket stuffers, was in a Maxpedition Fatboy-S "man bag" slung over my shoulder. My ID holder was in my t-shirt pocket. He was able to observe me removing the ID from my shirt pocket. He asked me to removed them from the holder before handing them over. I did so. He asked where the gun was; I pointed to the man bag which was on my left side, slung over my left shoulder. He asked me to not go there during stop, and I smiled and said "no problem." He thanked me, and the stop went smoothly.
Now, here's why I no longer use that ID holder.... I'm 58 years old, and I used to smoke a lot of pot and take LSD back in the 60s and 70s, and I find that many of my brain cells are pitiful and tattered smoking ruins of their former glory. On several occasions before leaving the house, I did the inventory check: "spectacles, 'manticles,' wallet, and keys," ....check! Status? Good. OK, let's roll. I get to my destination only to realize that my ID holder is still back on my dresser at home, and here I am, sporting a loaded gun around with no ID onboard.

After having done that 2 or 3 times over a two year period, I decided to put my IDs back in my regular wallet—which I never leave at home because I always pat my pockets and do my "spectacles, 'manticles,' wallet, and keys" inventory before leaving. However, the change-up demands new procedures if stopped by a cop. What to do? Here's what I came up with......
Like a lot of guys, I carry too much crap in my wallet, consequently, it's not nice and flat, and sitting on it is like sitting on a softball. (Only the Lord knows why I feel the need to carry my NRA card or my CVS pharmacy discount card around, as well as other sundry rarely ever needed items such as Costco/Sam's Club/Gym Membership cards, but I am a typically confused male....) Anyhoo... My car has a sort of pocket located in the top of the left armrest on the driver's door, just behind and below the inside door opener. So when I get into the car, my wallet goes into that pocket on the armrest. It is immediately visible and available if needed; it is held securely while driving, my poor back doesn't have to suffer the slings and arrows of sitting on it, and I have to set my hand on it to open the door, so I don't forget it when I get out of the car.
Hopefully, I won't have to test it for another 5 years.
Oh... and I don't argue with cops or try to make their job harder than it needs to be because that's just dumb. Arguing with a cop simply escalates the situation and you can never "win." They can respond to my escalation by calling backup. I can't get backup until after I'm booked in, and it costs a LOT of money....which I don't have much of. Plus, I'm willing to entertain the possibility that maybe, just maybe, I might have done something wrong. I truly do not understand people who get their back up at the slightest perceived insult to their "sovereignty" and turn it into some kind of drama queen confrontation. Perhaps it's because I believe that only God is truly sovereign, and it is my calling to submit to that truth each and every minute of each and every day.