When first opening the course or people admin search tool, the message displayed is "No courses found" / "No users found". Depending on how long these pages take to load, the user may be under the impression that the courses and people pages are not working.
When searching, either the same messages continue display, or if the pages actually loaded results from being opened, the user is looking at the initial load with no indicator that a search is actually being performed.
Suggestions for both courses and people:
When opening the page, display a "Loading..." message until results are displayed
When searching, display a "Searching..." message until results are displayed