How did the phrase thinking with your Johnson originate?

It is not known exactly where the term "Johnson" originates. The most likely theory is that it refers to the Johnson Bar that was used to control steam trains from the early 19th century (and is still used today in many types of vehicles). Johnson bars are also used in re-enforced concrete (invented by L. A. Johnson). Nevertheless, the phallic symbolism is clear; Johnson refers to a man's penis.

Thus thinking with your Johnson means to think with your penis, rather than your head.