I"m not sure how thing work with private employers, other than the fact they can fire you without any reason, or any reason they choose, as long as it is not one of the legally protected things like age, sex, race, etc. Even if you parked on private property and walked a half a mile to work, they could still fire you. The law offers no protection from a private employer when as an employee you violate their policy in regards to having a firearm in your vehicle.
If you worked for a local unit of government, then they only have the authority to ban firearm possession basically anytime that you are covered by workers compensation. This is actually quite complicated because we have to rely on court cases to determine when you are or are not covered by workers comp.