If you feel that you have special abilities or qualifications, I would suggest contacting the local SAR organizations and discussing with them how best to make use of these skills.

As far as using psychology and intuition to (presumably) try to predict where the lost person might be, there is a considerable literature on this, I believe. SAR organizations will normally try to build up a profile of the lost person. Children under 5 will typically behave in one way; teenagers will typically behave another. Is the lost person an experienced outdoorsman/woman? a hunter? hiker? backpacker? risk-taker? All of these will likely influence the type of search.

If you study up on the psychology of lost persons, then you may reach a level of expertise that will be of value to a SAR organization. If you walk in without doing any background research, assuming that a BA in psychology is all you need, and get interviewed by someone who really is an expert in this area, you will most likely get relegated to the role of "warm body".

Check out the NASAR bookstore, especially their books "Fundamentals of Search and Rescue" and "Advanced Search and Rescue" - I believe one or both of these has a section on the psychology of lost persons.
http://www.nasar.org/garmin/default.php?cPath=19&parent=9

You might want to see if you can get a copy of "Lost Person Behaviour" by Kenneth Hill. See Professor Hill's home page at
http://husky1.stmarys.ca/~khill/
or at
http://www.sarbc.org/k-hill.html
(Hill is a Professor of Psychology at Saint Mary's University in Halifax, Nova Scotia, who has a particular research interest in Search and Rescue.)