Calc 7.3.5.2 LibreOffice Community.
In any spreadsheet, press F5. Navigator child window should appear.
Press any navigational key - tab, shift+tab, left, right, whatever. Unfortunately, keyboard access is sent to the spreadsheet, instead of to the navigator child window. This completely defeats purpose of having the navigator in the first place. If you need to use a mouse to use the navigator, then you don’t need the navigator (you’d use other GUI objects instead).
The Navigator box would benefit from a re-design to make it slicker. The typical user of the Navigator window is a keyboard user who uses named ranges like bookmarks. The default control of the Navigator should be an edit box, ready to accept either a named range or a sheet-and-cell reference. For inspiration, please refer to the Excel equivalent.