When I search from Leader Resources in the Handbook search box, I still get results returned from Handbook 2, mixed in with results from other resources. It seems to work exactly as if I had typed in the search string in the main LDS.org search box.
But that search box used to return results from only the handbooks. The user interface there clearly implies that it will do so. Furthermore, it returns no results from Handbook 1, even if you are authorized to view Handbook 1 online.
You can still go to Handbook 1 and do a search from there, but the Leader Resources search box doesn't let you search it.
Update: The previous sentence is not correct.
Questions that can benefit the larger community should be asked in a public forum, not a private message.