Debug Mode writes search and indexing operations to the PHP error log, which is the fastest way to see what the plugin actually did when something behaves oddly. The toggle lives under Elevated › Site Search › Settings › Advanced Options, in the Indexer section.
Navigate to Elevated › Site Search › Settings, expand Advanced Options, and switch on Debug Mode (“Log search and indexing operations to the error log”). Save.

Run the search or rebuild that misbehaves, then read your PHP error log. On sites with WP_DEBUG_LOG enabled that is wp-content/debug.log; otherwise your host’s error log. Entries record what was searched or indexed and when.
Debug Mode is for diagnosis, not for everyday running: turn it off once you have what you need so the log stays readable.
No entries appear in the log. Confirm the toggle saved, and check which error log your PHP writes to; hosts route it differently. With WP_DEBUG_LOG set to true, entries land in wp-content/debug.log.