Reverse on itself is the same as switching back on itself. If you were traveling north on the side of the mountain and you encountered a curve that sent you back south, this would be an example of the highway 'switching back on itself.' This type of curve is called a 'switchback.'

The passage is badly written, in my view. I had to google "switched back on itself" to make sure it even exists! I got a mere 11,400 hits, which suggests that this useage is not standard. However it's (just) understandable as "tightly winding back and forth". By the way: the title of this question needs some work: never start a question with "how to". Instead, say "how do I/you..." For example: "How to do this?" (wrong) --> "How do you/I do this?" (right)

I don’t know if I’m adding anything to what’s already been said by the others. Normally a thing can’t be “on itself”. I can sit on my hands, but I can’t sit on myself. An object can be placed on another object, a vase on a table for instance, but it can’t be placed on itself. If the meaning of “on” is about a spatial relationship then “on itself” would probably often (if not always) mean that the normal shape of a thing had been somehow distorted/altered so that a part of the thing was in physical contact with another part of the thing. The thing would be “on itself”. If you took a rod made of a flexible material and bent it so it touched itself you could - in my opinion - say that it had been bent (in) on itself.