Verified answer

The border patrol is a federal law enforcement agency. It is not a physical place and therefore it is impossible to drive your car through it. In order to enter the country, you must drive through a port of entry where you and your vehicle will be screened by Customs Officers. Customs is not the same as the Border Patrol. Unless you do something very very bad you will probably not see any BP Agents. All vehicles and people are screened by Customs on one way or another regardless of citizenship. Not all vehicles are searched. At the ports they may use their discretion to search vehicles and persons without any probable cause.

your citizenship status means nothing you will be checked going back and forth through the border.

they do random checks