Ground vehicles are really problematic at an airport. The problem is not so much a matter of regulation as a problem that the people driving the vehicles sometimes are unfamiliar with flight processes so they create hazards without really understanding the danger they are creating. The "regulations" are that nobody is supposed to be on taxiways or runways without approval whatever that means, but since the FAA cannot revoke the license of somebody that does not have a license, it's a toothless rule. Also, the typical runway intruder does not even have a radio, so getting approval is problematic for them. Cops are the worst offenders. I have seen some very dangerous situations evolve from ignorant cops with no idea what they are doing just driving onto runways acting like they are god or something.
The main way the FAA interfaces to the ground control problem is to publish a lot of safety guidelines hoping that somebody will read them. Some airports have elaborate safety training for ground personnel, but the main risks usually come from untrained personnel at smaller airports where there is little or no training.
This is one of the main reasons why most airports work hard to get good fencing set up, so some bozo does not drive onto the runway.
In general, ground control takes care of authorizing vehicle movement and utility trucks are supposed to coordinate their actions with ground control. In untowered airports, utility trucks are supposed to call on CTAF to notify nearby pilots what they are doing, but unfortunately most do not have radios. Once I was landing and there was some truck on the side of the runway because the guy was removing a turtle or something. The truck had flashing lights so it was easy to see luckily.