In forensics, there is a well-known principle named 'Locard's Exchange Principle. This principle broadly states that people who commit crimes will leave with parts of the crime scene with them - traces of the environment but they will also leave something behind - skin or traces such as fingerprints.
I would like to broaden this out to the human mind since the concept of an MO (modus operandi) is also well-known whereby a criminal usually acts in a consistent manner across crime scenes.
The human mind may, I assume, may also have a principle akin to Locard's. Our entire self is built from a complex interplay of genetics and environment and this interplay can contribute towards the personality of an individual.
When a criminal acts, they act not from a blank slate but with all of this mental baggage and so it cannot be surprising that in any crime scene they leave a part of their mental life as well as parts of their physical presence. Emotional traits and vulnerabilities may be detected in the way the criminal treats others or the environment in which they commit their crimes.
These mental traces may be the mortar from which an astute profiler may build a working understanding of the individual. Understanding how Locard's principle may be thought of as a mental and not just a physical taking away or leaving behind of a trace may aid in understanding an unknown criminal and thus lead to their capture.
For more information on Locard - http://www.forensicsciencesimplified.org/trace/principles.html
It's a good piece. Its very well written, I agree with it. Locard's exchange principle is the first thing we study when we chose forensic sciences and it has such a vast perspective as you described here yourself. Human beings are complex, their minds are like a maze and that maze is just bigger and more complicated when it's the mind of a criminal. Understanding a bit of that maze using Locard's exchange principle can aid the authorities in the process of getting to that person faster. I back this theory.