Search function on smart phone & iPad / Tablet in Vertical mode

Hello. When running my site on my iPhone, or my iPad in vertical mode, the menu bar disappears in favor of a search button. For me, this brings up what looks to be the full list of pages from the demo install (pic attached.)

Is there a way to show the menu bar in this state instead of the search button? If not, is there a way to customize this “search sidebar” to show only menu items?

Thanks!