For the SQL Server data source, you should be able to enter exactly what you normally would when connecting to your database via a program like SQL Server Management Studio. So if you normally use (local), you should be able to use that to connect to your database instance.
I have attached a screenshot of Application Authentication Settings screen from the TeamPulse installer. Can you please send us a similar screenshot showing what you entered? It would also be helpful to show a screenshot of what you use to connect to your database via SQL Server Management Studio.
the Telerik team