This approach was considered early this year and last year. It has some merit but allow me to play Devil's advocate for a minute. Suppose your boss suspects you to have stolen some company property and placed it in your car. Right or wrong, he can call law enforcement. Let's also say a fellow employee will support his claim and say you put the property in your car. Now there is probable cause for LAW ENFORCEMENT to search your car. So let's also say, (because you did not in fact commit the theft) the item searched for was not found. However, in the course of the search, it is found that you have a firearm in the car. Law enforcement will not care about the gun as long as you possess it legallly and have a permit. BUT your boss now KNOWS and even though it was not the object of the search, you will still be toast.
The only way for something of that nature to work would be a law that prohibited an employer from making vehicle searches a term of employement so you could refuse to allow a search without loosing your job. Second, the employer or any of his representatives or persons acting on his behalf would have to be prohibited from being present during a search conducted by law enforcement and then law enforcement could ONLY report whether the object of the search WAS or WAS NOT found. Anything else found in the course of the search, provided it is legal, could not be reported. NEXT, if by some way the presence of a firearm was found out by your employer when it was NOT the object of the search AND your employer took ANY action relative to items found in your car, then the employee would have legal recourse against the employer. But I kind of doubt that if we can't get a parking lot bill passed, a law like this would never pass either.
Second, as far as I am concerned, HCP holders have LONG SINCE proven their trust worthiness. The time for that has passed. We are approaching 20 years of Handgun Carry Permits in Tennessee. How long should we have to wait to be considered vetted.