Ok, I solved the problem. I think this is new behavior from the last version of Safari. But this is what I have found out.
In order for the magnifier to activate and open the Finder window, the item to be located in the "Show Downloads" drop down must be highlighted by clicking somewhere in the row where it is listed. In my setup this highlights the item in blue and then clicking the magnifier will open the Finder window. If the item is not highlighted, then clicking the magnifier does nothing, even though the magnifier icon itself indicates feedback that it has been clicked.
Like I said, I think this is different behavior from the previous version of Safari and thus it takes 2 mouse clicks to open the Finder window rather than one.