This is implemented in 4.1.x.
Hover: Highlight the hovered item (as in prior versions)
Up: Move up from the current highlight. If none is highlighted or beginning was reached, jump to last item.
Down: Move down from the current highlight. If none is highlighted or end was reached, jump to first item.
Page Down/End: Jump to last item
Page Up/Home: Jump to first item
Enter/Click: Click the selected item
Esc: Close the search dropdown
All other keys still type in the search box. Highlight is preserved if you type more text and the filtered results still include the highlighted item.