TFS Installation Fails over to mirroring secondary despite not having a Fail-over partner specified
Specifying Failover Partner in the connection string is only for an initial connection.  After connecting the client is notified of the failover partner, and will use that for reconnecting in case of a failover.


  [After connecting to the principal] the data access provider downloads
  the server instance name of the current mirror server. This name is
  stored in the cache as the failover partner name, overwriting the
  client-supplied failover partner name, if any.


Connect Clients to a Database Mirroring Session

So even applications not specifically configured for database mirroring will discover the failover partner at startup.


  our TFS installation has no failover partner specified


So on reboot or cold start TFS will fail to connect if server specified in its connection string is not available and hosting the principal database.  But if a failover occurs after TFS has succesfully connected to the principal it will know to reconnect to the failover partner.