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First question is are people even using the search?
I don't think there is a core function for logging search activity. That would further burden the server and cause more queries.
However, all the activity is contained in the server logs outside of xoops. It is wise to invest time (maybe money if time is scarce) in a good server log analysis system. You should have access to the backend server logs and in there is most everything you need. It could take time to filter the logs for very specific trends like search terms used but once done you are gold for the next time.
Search your logs for search.php and see if the terms are there. Then you can work on a reporting function that is informative. BTW, this is done outside of xoops, stand alone. It can run along side XOOPS in a unique directory for presentation.