Forgive me, I do forget as it has been a decade or more but...
The company that I was previously employed by had a weapons ban and they also had a vehicle search consent policy. These were signed by all employees at time of initial hire including drug screens etc...
I have had my vehicle searched, along with all other employees at that particular location, coincidently in Norfolk. This subject did come up while talking to a lawyer freind and she explained that VA law, at least at the time, did not prevent the company from doing searches as everybody had agreed to it when they had hired on.
As a side not, that particular company largely overlooked any weapons in vehicles, due to the type of people we generally hired, as they were usually hunters, fishermen, etc that enjoyed shooting and other outdoor sports. Never worked a nuke plant, always WTP or WWTP. But a bunch of the crew in Norfolk had worked Surry!!
My point is, if my employer asks me to not bring firearms to work, I agree that once I am on his/her property I should grant those wishes by not being armed. If I leave my firearm secured and hidden from plain view, I am unarmed. I should also still be able to defend myself on my way to and from my place of employment. And I thank TN for progressing this law that will allow that regadless of an employers view.