That style driving is called the “jerk line method”. Leaders turn right, left, stop, by how many jerks on the (old days) rope held by the Teamster on the Wheel animal. Being Freighters, you made money by how much load could be moved in the wagons, so driver weight could be carried by the animal instead of on the wagon.
The Borax folk had their own system worked out for moving the borax from mining site to the shipping location. Did not follow other companies ideas. There were several people making the trip, not just the teamster, so animals could be cared for on the trip, along with keeping the men fed. Heck harnessing 20 mules each morning, unharnessed at night, fed and watered, probably all feisty mules, is going to take a while! One man could not manage the job and get on the road in a timely fashion.
The Conestoga Wagon drivers of early freighting history used the jerk line method of driving long before the West got explored. They were the ones using Team bells on their 6-8 horses to warn others they were coming on the trail. This is the origin of the old saying (many versions) “We will be there with bells on”. Having no bells on arrival meant there was trouble along the way and driver surrendered his bells to the person helping him out.