Back to the suggested scenario - I would feel a duty to at least let the guy know he's showing and since that means I'm gonna have to make contact with him, there are certain things I've got to be aware of and try to accomplish in the meantime, but I'll skip most of those. (officer safety issues)
But then again, around here, everything may change if he's wearing an open carry type holseter and it's just a jacket riding up. I would probably note weather the gun is nice or junk and forget about it. Only a purposefully hidden gun will draw my attention in Wyoming.
But if it is a concealed gun - First - I'd wait until he's seated at a booth before approaching. Then I'd walk over to his side and introduce myself - "Hi, I'm ______ and I would like to talk to you..."
Next I'd let him know that I'd seen what he had in his back pocket and ask if he had a CCW permit (note: not ask for it)
What I'd expect of the sloppy carrier - Up to this point hopefully he's surprised , but keeps his calm. (and continues to do so) Just sit there and listen, under no circumstances should he reach toward the already spotted firearm. Sigh - folks do silly things sometimes.
My actions - if the answer is "Yes, I have a CCW" - then I ask if it is in the same pocket. If "yes," advise him what is a silly place to keep it since I need to look at it now and really would prefer he not be grabbing things out of the same pocket. Hopefully I won't get a blank stare. Then I would ask for name and date of birth to do a DL check, hoping the CCW shows up there. If not, I'll have to retrieve his wallet or whatever holds his CCW permit to check it. He's not going ot be allowed to reach back there - "Sorry sir." Check the permit.
If the answer is "No I don't have a permit to carry concealed," I'm going to have to take stronger action, the first of which is to handcuff him and secure the weapon. We'll see if he needs arresting later orf at least a citation. It all depends on his story.
If everything is OK and the guy turns out to be just a sloppy CCWer, I'll swap a few carry tips with him, so he doesn't run into such a problem again, and wish hiim good day.