It's my understanding, that when encountering a funeral procession, you are not supposed to break the line, or try to pass the procession, unless you are on a divided highway. Funeral processions are not emergency vehilces, but they have the right of way, once the procession starts to move through an intersection. The hearse, or the lead car can not run a red light, but once they go through, it's like a long train.
Cars do not pull off the road for a funeral procession, in my area. Even if it's on a two lane highway.
I have been in processions that traveled long distances on divided highways and have never seen anyone pull off the road or refrain from passing the procession. These processions always move at the minimum posted speeds.
I have more problems with people who are in the line that don't understand the rules of the procession and either get confused when a light turns red, in the middle of the line going through, or who stops for the light. It should be the responsibility of the funeral home to instruct the drivers before departure, but I have never been instructed anything other that "Please turn on your lights and follow the car ahead of you. "
Doc