The Search Our Website Option
Search our site - Using the Search Bar - Magnifying Glass
"Desktop mode" users should see the search bar option magnifying glass icon (see attached) at the top right of the screen in both Portrait and Landscape orientation. Examples 1 & 3
Example 2 shows that Mobile users may have to turn/rotate the device (temporarily) to landscape mode to access the search bar.
Sample 4 shows no magnifying glass on a phone until it is either turned sideways or have the "Desktop site" option turned on.
The reason the search bar might appear in landscape mode is due to the website's responsive design. To fit on a smaller vertical screen, this website, using Google Sites, is hiding elements like the search bar within a menu. By rotating to a wider, horizontal view, the site's layout expands and makes the hidden elements visible again.