I'm not quite sure I understand this -- please bear in mind I am self-taught in SQL and .NET.
I see proof here that the databases are in sync. What I don't see is proof of automatic failover, at least as I understand it (I'm probably wrong). If I have an application on a workstation that relies on an ODBC connection to a SQL Server (Instance1), and Instance1 goes down, will the ODBC driver automatically point to Instance2? Or will it need to be reconfigured to Instance2? If ODBC has to be reconfigured, how is this "automatic failover"? Unless it's just the fact that the new server is available for use immediately?
By automatic fail over in mirroring what we mean is the backup database will be up and running without any manual intervention unlike in log shipping.
Now coming back to your question, the thing you are trying to achieve can be done via SQL Server Clustering and not mirroring. Let me explain. Say your application connects via ODBC connnection to Database Server "SQLVM01", as in that is the server value fixed in the connection string.
Now in clustering setup we have 2 servers Srv1 and Srv2 both are clustered as "SQLVM01" to represent 1 Server. They are in Active/Passive formation i.e. Srv1 will be alive and active and Srv2 will act as fail over. Your app will keep connecting to the same server but internally if Srv1 fails Srv2 will automatically take over without any interruption. Thus there not any connection changes required to be done by the apps.
Mirroring will still require the Apps to edit their connection string but nothing will be needed to be done for getting the back up database alive and active as that will happen automatically. While in case of log shipping you will need to also perform database fail over and then edit your app connection settings to point to the new server name where the DB is hosted.