What if the event from clicked button arrives _before_ the `focusout` event?
What if computer is very slow and it takes more than 0.1 seconds between `focusout` event and `click` event?

Can we come up with a more robust way of controlling focus? Is it possible to check in this function whether focus is now on one of the search buttons or elsewhere? If you could do so, you can just call `clearSearch_` straight away.