Hi Phillip,
The menu which provides the search box uses a template (mod/glossary/templates/standard_action_menu.mustache) to create the available items which is good news. Templates can be easily edited by some who understand HTML well without other coding experience. The revised template can be placed in the theme where it will override the core template making upgrades more easy. The existing search there could be replaced with a HTML form that directs to global search instead of the glossary. An experienced developer should take a couple hours to do this with proper testing.
The menu which provides the search box uses a template (mod/glossary/templates/standard_action_menu.mustache) to create the available items which is good news. Templates can be easily edited by some who understand HTML well without other coding experience. The revised template can be placed in the theme where it will override the core template making upgrades more easy. The existing search there could be replaced with a HTML form that directs to global search instead of the glossary. An experienced developer should take a couple hours to do this with proper testing.