They can't arrest a person for a traffic violation and then have PC to look for a gun. Your example was a good illustration of that. There has been some changes when an officer tries to search based on securing a scene which was argued in Gant v Arizona 2009 USSC.
I really liked when you asked him for a business card. Cops don't have business cards they aren't selling a service or product; they have badges that identify them! What was up with the documents he asked for and you say you have but can't find but don't think you have them? That made sense. ...
Before it goes and the car will start, but once gone car will not turn over fo no matter how long you wait.