It was the "Integrated Security=SSPI;Persist Security Info=False;" actually more precisely just the "Integrated Security=SSPI;" that was forcing the connection to the Windows logon instead of the SQL Server user logon specified in the connection.
SqlConnection myConnection = new SqlConnection("Integrated Security=SSPI;Persist Security Info=False;Initial Catalog=FPY;Data Source=MyServer;User ID=PartsetupUser;Password=MyPassword");