There are a few different ways to utilize a support vehicle while on tour. It sounds like you are thinking of "direct follow support" where the vehicle drives directly behind the rider. This is used in ultra-races such as the Race Across America (RAAM) in order to give the rider easy access to required food and water, to provide music, directions, and moral support for the rider, to carefully watch the rider's physical and mental condition, to provide lighting at night, and to have spare wheels and bikes ready for the rider. For touring, however, I think this type of support is inappropriate. The goal of the direct follow is to keep the racer on the road as much as possible, but the true joy of touring comes from stopping. Also, it requires a very dedicated person driving behind you and is very stressful on the driver and anyone else in the car, so it takes a very special person to be able to perfrom this type of support well.
Another ultra-race style of support is "leapfrog support." In this, the support vehicle frequently stops at the side of the road and waits for the racer to pass, again supplying anything they need to keep them on the bike. After the rider passes, the vehicle drives up the road at the normal speed of traffic, passes the rider, stops again, and repeats. In a racing context, the real trick to these is for the support vehicle to wait long enough at each stop after the rider passes so that the support vehicle keeps the rider mostly in front of them, it does no good if the rider has an issue while they are behind the vehicle. Again I think this style is inappropriate for touring, especially the racing oriented quick leapfrogs where the support vehicle tries to leapfrog the rider at least every 15 minutes.
Tour groups that have a dedicated support vehicle most often use them to carry the riders' luggage, to set up lunch and water stops, and to generally keep tabs on the riders so that no one gets too far off course or has a serious mechanical issue without support. Again, the real trick for the driver is to keep most of the riders ahead except when setting up the rest stops.
If you have friends or family who are interested in making the same trip that you are by bike, they may be willing to carry your luggage and meet you each night at the hotel or campground. This gives them the freedom to explore and do other things during the day rather than looking at the rider's backside, and lets you enjoy the ride with less gear and without worrying about the people in the support vehicle. Maybe you can meet for lunch as well, or carry an overnight bag and meet the following day. Remember, the tour should be enjoyable for everyone, the riders and the support crew.