The Showkase root directory's 'index.php' file is used (to display the Showkase home page) only when the Showkase site is accessed via the root directory (without specifying an actual page name).
Every Showkase page has its own folder in the Showkase root directory (and an 'index.html' page inside the folder).
For example, a Showkase page named 'my_page' will be located here: http://www.example.com/showkase/my_page/index.html
However if the designated Showkase home page is 'my_page' and a visitor to your site goes to: http://www.example.com/showkase/
... then the 'index.php' page will be used to show the '/my_page/index.html' page.
That's really just an aside about the function of the root 'index.php' file. (Your tags should not go in this file).
If you want to have all your own <link> tags included on all your Showkase pages, then the best place to put them would be alongside the existing <link> tags in the /showkase/_themes/base/pagetypes/basetheme.tpl file.
Open the basetheme.tpl file in a plain text editor, scroll down to the {block "stylelinks"} section and add your own <link> tags alongside the other ones there.
All you now need to do is republish your site for all your own <link> tags to be added to all your Showkase pages.