Failed SEARCHES aren’t recorded without a third party tool. Behavior Tracker from Mondosoft allows you to track the effectiveness of search.
As for the Gatherer log, for failed indexing operations, the best thing is probably to turn on logging for successful and unsuccessful operations from the UI then use the NGTHRLOG.VBS file to dump the contents into a CSV that you can open with Excel. NGTHRLOG.VBS is available from Microsoft Product Support Services at no charge.