I worked with a criminal psychologist during my time in law enforcement. While I can't speak to it from personal experience, I did have several conversations about their day-to-day, and I observed what they did for the job.
For one, it isn't like "Criminal Minds" or other similar TV shows. Most criminal psychologists are tracking crime trends across entire areas, not generally focused on tracking specific murderers. Even this criminal psychologist worked for a federal agency, and described themselves as more of a generalist instead of focusing on a very specific thing. Another thing to note is the teamwork aspect. Most criminal psychologists work on their profiles independently, then present the findings to a team. They obviously consult with each other, but generally aren't all teamed up working on the same case or profile.
The other aspect to this job is contracting. I know the profession can exist outside of the agency itself, be a private organization, and come in for consultations with departments. This can be a great way to work if departments in your area are all too small to afford their own full-time criminal psychologist. This way those departments can get the services on-demand, because they generally may not need them for years at a time otherwise.