Update: Please ignore the below. I had disabled the menu icon on the landing page header instead of the search (don’t know how it was still showing though) and therefore didn’t have that option available. I’ve fixed it now.
Your solution works but not for the landing page as it uses a different header. I suppose this is so it can be transparent for the slider.
In fact the (Theme Options > Header Builder > Mobile menu > Dropdown Opening Action) is not available for that landing page header builder.