All they need is a sign saying "All vehicles subject to search." They probably wouldn't even need to do that- they could just post a security guard at the entrance and forbid entry to anyone who refused to consent to a search. Rules in employee handbooks authorizing searches of vehicles are common and fully enforceable.
Nor can private citizen arbitrarily strip another of their Rights.
You have no "right" to enter another's property in violation of their rules.
If they have the parking lot open to the public, then they also have to respect the equal Rights of those individuals that will come along with it.
So, do you have the right to hold a political rally in your employer's parking lot?
No. Actually. They are not fully enforcable. Depends on local statutes and case law. In many places, they have been found to be exactly as I describe them, violations of the property owners Rights. Namely, the car owners.
You have no "right" to enter another's property in violation of their rules.
Ah, so if they make it a rule to engage in homosexual sodomy you'd be fine with that? Don't be silly. A private entity can no more strip a person of their inalienable Rights than the Government can. It violates the very premise upon which this country was founded.
So, do you have the right to hold a political rally in your employer's parking lot?
If it was a rally inside my car, sure. It'd be an awefully small rally though.