Configuring non-configurable widgets in 2.2

Hi,
I’d like to edit the WordPress search widget because it is causing validation errors. But it has no configuration options in the sub-panel. Where does this search widget actually live so that I can edit it? I’ve seen others posting similar questions, but no answers so far that I could find.

In general it would be useful to know how to edit widgets that aren’t editable in the widgets subpanel.

Thanks in advance!