Look bro, they can not search your car without your consent, regardless of any sign or policy. Now if they decide to fire someone for refusing a search of their vehicle, they better have credible evidence on that employee for probable cause or that employee will most likely be getting a nice settlement. They can't just arbitrarily demand a search for anyone's Vehicle at anytime. It just doesn't work that way.
Here's the deal, I said it is a condition of employment...Don't get hung up on the semantics of words. You are arguing
rights, I'm saying
condition of employment, they are different, and can overlap, but not one in the same.
Here are some other conditions of employment, that if you don't follow you'll be terminated.
You must wear a proper uniform,
You must have a current license,
You must wear all black shoes(YMMV on this one depends on management)
So sure, They do not have a right to search your vehicle.
But, They
do have a right to fire you if you refuse to let them search.
They can fire you in any one of the 28 Right to Work (AKA Right to Fire) states
and they don't even need a reason, they just say goodbye.