Is there a reason something like this wouldn't work?

CREATE TRIGGER CheckReportsFinished ON dbo.ReportStatus

AFTER INSERT

AS

DECLARE @COMPLETEDROWS INT = 0

SELECT @COMPLETEDROWS = COUNT(*) FROM dbo.ReportStatus WHERE [success flag] is not null;

IF (@COMPLETEDROWS = 20 )

BEGIN

-- just an example here

RAISERROR ('Report Status TRIGGER ACTIVATED.', 16, 1);

-- you will probably want to use

-- EXEC msdb.dbo.sp_send_dbmail instead

-- but this requires configuration before you can use it

END;

GO