Open search dialog, search and create a list of results, observe that F3 moves through the list of results.
Close Search dialog, observe that “Show Next/Previous…” menu items are still active. Yes, thank you, doing this directly in my scripts would be very useful!
Sadly, pressing (shift)F3 does… nothing. Is this on the list to be fixed, or are the active menu items a bug? I would hope the former.