How to use the navigator tool to show layer A in real-time when another layer B is still selected.

Hi, the navigator panel will show a reduced view of your document, its goal is not to show a different state.

similarly, Window>Arrange>New window for [document title] in the view menu can let you preview the document with a different profile, or a different magnification, but will synchronize the state (layers shown) of the document.

what are you trying to achieve? Are layer A and B affecting each other's via blend modes, etc? 
if not create a new document and copy layer A to show it as you work on B. Window>Arrange>2 up vertical to show them side by side.