Meantime, a very temporary hack is this: change the type of the search-input element from “text” to “search”: e.g. <input class="search-input" type="search" placeholder="Type to start search...">
That will give you an “X” in the search box that will indeed clear search results.
When you do that, the search box will look a little funky, so you’ll probably want to add a couple lines of style to the .search-input css such as: padding-left: 5px; height: 30px;