G'day,
I'm a javascript expert and would have no trouble at all implementing a search bar for you. It would be built on a powerful, standard search library eg. google or elastic search, and then contain add an additional layer on top to capture the entered search terms. The terms could then be compiled into csv format as date - value pairs and emailed to the administrator at regular intervals. If you could tell me more about the layout/design of your website then I will be able to provide you with additional implementaion details. If you have an questions please don't hesitate to ask.
Regards,
Justin