May our new Constable make traffic stops in his unmarked privately owned patrol car?

Chapter 721 Transportation Code says he needs the Commissioner's permission to do so in a County owned vehicle, but I can't find any statute or rule that addresses what he may do in his privately owned patrol car.

I don't think you'll find a statute specifically addressing authorization to make traffic stops in an unmarked private vehicle. We looked into that during our never-ending constable litigation. What your constable is likely to encounter, though, is folks who -- being cognizant of the sometimes dangerous society in which we live -- are unlikely to yield to his authority. If someone in an unmarked car pulls up behind another, turns on a light and motions to pull over, absent any markings or exempt plates to indicate official status, the odds of an uneventful stop are less than strong. Besides, if the car is unmarked and privately owned, what will be the consequences of someone failing to comply? Evading requires knowledge that the person attempting to detain is a peace officer who is attempting a lawful detention. Most law enforcement agencies have policies dictating that routine traffic stops are the province of marked units. There's good reason for that line of policy.

I know that at one point police vehicles were required to have their department identified in a minimum of two inch letters in a color contrasting to the paint in order to perform traffic stops. (It came up with the Brazos County Constables). It's been several years and I can't remember which code the requirement was located in.

I also believe that in Montgomery County the deputies personally own their patrol cars and are paid a vehicle allowance by the County.