"Probable cause" seems like a very open statement
In the simplest terms, probable cause means, an officer knows of facts or circumstances that would lead a reasonable person to believe a specific crime has been, or is going to be, committed at a specific location. In the case of a firearm in plain view in a vehicle at a traffic stop the officer must have some facts that would lead a reasonable person to believe that the firearm in question was connected and related to that specific crime that has been or about to be committed at a specific location.
For example, you get stopped for speeding. A reasonable person would not believe that a firearm in plain view was related and connected to the crime of speeding.
Another example, you are in the immediate vicinity and time frame of an armed robbery. Your vehicle matches the description of the vehicle used in that armed robbery and an officer stops you. In this case, a reasonable person would believe that it is possible for a firearm in plain view to be related and connected to the armed robbery that just occurred at ______ location. In the course of the officers investigation of the armed robbery they would have probable cause to run the serial numbers through NCIC.
Another example, you are stopped for speeding. Upon approach, the officer sees a small part of a firearm and it is positioned in a manner attempting to conceal the firearm and you do not have a concealed handgun permit or the firearm not covered (rifle or shotgun) by the concealed handgun permit. If the officer can articulate you were trying to conceal the firearm, they would have probable cause and could seize the firearm and run the serial number though NCIC. However, this scenario, has more elements regarding what constitutes a concealed weapon.
This is very simple terms and probable cause can and is usually more complicated. Also an officers probable cause is the very first thing that is challenged in court. Because if the defendant or their attorney demonstrates the officer did not have probable cause, any and all charges after the fact are not valid and dismissed.
(The legal disclaimer, I’m not an attorney, nor did I play one on TV, nor did I stay in a Holiday Inn last night so do not use this information as legal advice 🤣)