Lots of anecdotal examples of this are cropping up elsewhere, and almost always the police are polite, professional, and calmed when notified there is a gun, while the driver keeps his hands on the wheel.
And, a noticeable number of times, having a gun means that the police officer just gives them a warning instead of a ticket(!) I suspect the reason being that police are learning that legal gun owners are not just law abiding, but are allied with, friendly and supportive of the police.
Though a special note, during the current unpleasantness, it is very wise to be extra controlled in your behavior during an encounter. For instance, keep your speech slow and clear, and keep it separate from your actions. That is, do not talk and move at the same time.
When ordered to do something by the officer, tell him where it is located, then tell him you will get it for him, and finally, announce *while* you are getting it that you are getting it, giving plenty time for him to halt you.
For example:
“May I see your license and registration.”
“I am carrying a licensed (or legal) gun with me.”
“May I see your license (and/or “where is the gun now?)”
“My license is in my wallet, in the left rear pocket of my pants.” (or perhaps) “My gun is in a holster in the glove compartment. My registration is in the glove compartment as well.”
“Please remove your license from your wallet and give it to me.”
“I am reaching for my wallet in the left rear pocket of my pants.”
“Please get your registration from your glove compartment, while leaving your gun in there.”
“I am reaching for my vehicle registration only in my glove compartment.”
All in all, it sounds very wooden. However, it is very calming to police officers. Something very good right now.
(Important note: during any police encounter, be very aware of any other police officers arriving on scene. While the first officer may be very relaxed, the new ones may still be very tense and nervous.)
Your description of the “wooden” police encounter patter, is exactly what I used to do when I was a young driver in the inner city.
No one had to teach it to me. I was a long haired lowrider, and interacted with the police on an almost daily basis.