Taxonomy Term Path to Search Running Drupal 7:

Problem: I have a vocabulary that contains a list of faculty, within each faculty member term page is a list of research interests (a separate vocabulary) that are clickable.  Currently they go to their individual term pages.

Goal: How can I make those "Research Interests" clickable and simply make it go to the search page with that term as the search query?
I see two options to achieves this.

The first one is to alter the page callback for the taxonomy/term/%taxonomy_term path through an implementation of hook_menu_alter. In the custom page callback, when displaying a term from your vocabulary, use drupal_goto() to redirect to the search page. And for terms in other vocabularies, you can re-use taxonomy_term_page() to preserve the original behavior.

The second option is to implement hook_entity_info_alter() to alter the uri callback of the taxonomy term entity type. In the custom URI callback, when getting the URI for a term of your vocabulary, returns the URI of the search page. For terms in other vocabularies, you can re-use taxonomy_term_uri() to preserve the original behavior.