SP2010 environment shows that the actual link for signing in
as a different user is /_layouts/closeConnection.aspx?loginasanotheruser=true
SharePoint 2013 removed from the UI
SharePoint 2013 removed from the UI
But link still exists you can use.
They remove it because this option uses an unsupported
browser feature which is unreliable and causes other issues. It is not
supported by IE10, Safari