It exists at the edge of his property. If you enter his property, you do so on his terms. No one is forcing you to enter his property - if you don't like his terms, you can always work somewhere else.
That is why the 2nd Amendment is a constraint on government, not individuals or non-governmental organizations. Government can force you to do things. An employer cannot. If your car is on his property, he cannot search that car against your will. But he can demand that you leave and terminate your employment if you agreed beforehand that he had the right to search cars on his property. That's the difference here - he has property rights because he does not have the force of government to search you.
I see. Now where's the vertical boundary, somewhere outside the solar system?. Does the moron employer get to demand airline companies check with him about any regulations he might issue? The vertical boundary is the vehicle's outside edge. "If you enter his property, you do so on his terms."
It's a parking lot. It's there so the employees can park the car, not so the employer can dictate social policy, ban things and otherwise run roughshod over employee rights. If the employer doesn't provide the parking space, he'll have no employees. The employer doesn't get to infringe on public, or others private property by forcing his employees to park elsewhere. The employer has 2 choices, allow parking, or not allow parking. The choice to allow parking does not entitle him to anything else.
"That is why the 2nd Amendment is a constraint on government, not individuals or non-governmental organizations."
The relevant topic is property right and Freedom off the job, not guns. Employees are entitled under the 14th to enjoy property right and Freedom w/o it being userped by employers. In particular their vehicles. Whatever the employees decide to take with them, for whatever reason, when they travel to and from work is none of the employer's business.
"Government can force you to do things."
They force employers to have parking lots, so their employees don't clog up everyewhere else with their cars.
"he can demand that you leave and terminate your employment if you agreed beforehand that he had the right to search cars on his property.">
This particular demand is no more a valid than demanding the employees give him a BJ.
" if you don't like his terms, you can always work somewhere else."
Wrong. If the employer don't like honoring employee rights, he can get the hell out of the US and go somewhere that welcomes tyrants.