How do I unset/hide certain fields from being indexed by the core search module?
Goto the Manage Display page for each content type (eg, admin/structure/types/manage/page/display).

Click on the tab for Custom Display Settings.

You will see the view modes that your system knows about.  Tick Search Index and save.

You can now configure which fields get indexed from the tab for that new display mode (eg admin/structure/types/manage/page/display/search_index)

Dump the search index from Configuration -> Search -> Search Settings ( admin/config/search/settings), and cron runs will re-index everything.  Or, do a drush -y search-reindex; drush -y search-index from the command line.

Start reading from node_update_index() which is invoked from search_cron(), and you will eventually see a node_view($node, 'search_index');, which is how that display mode gets used.