The only way to search tags is to click on the term on the bib record or in the tag cloud. tags are keywords and should be searched in the keyword search.
On export to Zebra, dump tags into a MARC field (I propose 950 for MARC21, with a repeatable subfield a). Then configure a new index in Zebra for tags that picks up that field.
Once that's done, we can add tag searching to the advanced search page, and even to the facets (perhaps configurable with a system preference).