I have configured a Lightning Community using the Build Your Own template. I wish to add a global search box like the ones in the headers of most of the built in templates, to allow my users to search for CMS content. This documentation implies that I should be able to use the Global Search Box component, however, it's not available for me to drag into the builder. Does it need to be activated or enabled?
So as it appears that you would need a custom one to place in here. Else it will use the default search component. You can try, if you're not seeing anything search related on your page, to update the settings to show all components but it also notes that some may not function well depending on page types.
If your template has a placeholder for search, then you can add the search via navigating to
Setup >All Community > Builder > Settings (4th Icon on left)
There, expand the theme by clicking setting icons next to the Theme Layout Component and choose the global search component or your custom search component.