Hi!
Other options (they have their own caveats but you can try):
- Search for "Special:Search/QUERY" in the pagecounts-all-sites linked
above (zcat DUMP | grep "Search/") - this can provide you results such as "commons.m.m Special:Search/Jnnjjjnnnnjnjjnbnjbnjnjj 1 5418" so you know 1 user seared for "Jnnjjjnnnnjnjjnbnjbnjnjj" in mobile, at 2016-05-15 13:00-14:00
I wouldn't rely on this. It looks like a bug that it is in public data and this will probably be gone soon. Generally, the current official answer to the question of "where one can get logs of the search queries for public use" AFAIK is "there's no way to get it without signing papers and going through procedures".