Relatedly, the Advanced up-arrow toggly button thingy doesn't work while a search query is set -- clicking it once scrolls down a little, clicking it again closes Advanced.

Maybe we should just hide it during search?

I think this issue is more generic. What should happen when "search" is cleared? Do we restore the previous context?

Imagine that search can be triggered by any subpage, for example go to chrome://md-settings/searchEngines (or chrome://settings/advanced), trigger search, then clear search. What do you expect.

Agreed that at the very least, even if we do nothing (leave advanced expanded), we should ensure that any "adnavced" related toggle buttons work.

These are good questions (that old Options bypasses by using modal dialogs instead of sub-pages). +tbuckley, bettes

We should keep the same behavior from Options:
1) When the user clears a search, "Advanced" should return to its previous state before the search began
2) The "Advanced" toggle should be hidden while searching

Since Options didn't let you search from dialogs, while MD Settings lets you search from sub-pages, we need to define new behavior. My preference is that when the user begins searching, we exit the sub-page and scroll to the top of Settings. We can forget the sub-page and scroll position.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/c72fd9a779aaf29554c3ba4e08ff58602eff54d8

commit c72fd9a779aaf29554c3ba4e08ff58602eff54d8
Author: dpapad <dpapad@chromium.org>
Date: Thu Aug 11 22:09:28 2016

MD Settings: Hide the advanced page toggle control during searching.

Also ensure that after the user clears the search results, the advanced page
returns to the expanded/collapsed state it had before searching.

BUG= 629696 
CQ_INCLUDE_TRYBOTS=master.tryserver.chromium.linux:closure_compilation

Review-Url: https://codereview.chromium.org/2236723002
Cr-Commit-Position: refs/heads/master@{#411429}

[modify] https://crrev.com/c72fd9a779aaf29554c3ba4e08ff58602eff54d8/chrome/browser/resources/settings/settings_main/settings_main.html
[modify] https://crrev.com/c72fd9a779aaf29554c3ba4e08ff58602eff54d8/chrome/browser/resources/settings/settings_main/settings_main.js
[modify] https://crrev.com/c72fd9a779aaf29554c3ba4e08ff58602eff54d8/chrome/test/data/webui/settings/settings_main_test.js