Amend TSQL to your environment, run the TSQL, restart the agent service and test (I find it easy to enter an incorrect username and password).
USE [msdb] GO EXEC msdb.dbo.sp_set_sqlagent_properties @email_save_in_sent_folder=1, @databasemail_profile=N'<TSQL_MAIL_PROFILE>', @use_databasemail=1 GO USE [msdb] GO EXEC msdb.dbo.sp_add_alert @name=N'Login Mismatch', @message_id=18456, @severity=0, @enabled=1, @delay_between_responses=0, @include_event_description_in=1, @job_id=N'00000000-0000-0000-0000-000000000000'GO USE [msdb] GO /****** Object: Alert [Login failed : State 5] Script Date: 24/03/2020 12:50:49 ******/ EXEC msdb.dbo.sp_add_alert @name=N'Login failed : State 5', @message_id=0, @severity=0, @enabled=1, @delay_between_responses=0, @include_event_description_in=5, @category_name=N'[Uncategorized]', @wmi_namespace=N'\\.\root\Microsoft\SqlServer\ServerEvents\MSSQLSERVER', @wmi_query=N'SELECT * FROM AUDIT_LOGIN_FAILED WHERE State = 1 OR State= 5 OR State = 8 OR State= 14 OR State= 38', @job_id=N'00000000-0000-0000-0000-000000000000'GO USE [msdb]GO /****** Object: Alert [Error 823] Script Date: 24/03/2020 12:51:12 ******/EXEC msdb.dbo.sp_add_alert @name=N'Error 823', @message_id=823, @severity=0, @enabled=1, @delay_between_responses=60, @include_event_description_in=1, @category_name=N'[Uncategorized]', @job_id=N'00000000-0000-0000-0000-000000000000' GO USE [msdb] GO /****** Object: Alert [Error 824] Script Date: 24/03/2020 12:51:33 ******/ EXEC msdb.dbo.sp_add_alert @name=N'Error 824', @message_id=824, @severity=0, @enabled=1, @delay_between_responses=60, @include_event_description_in=1, @category_name=N'[Uncategorized]', @job_id=N'00000000-0000-0000-0000-000000000000'GO USE [msdb]GO /****** Object: Alert [Error 825] Script Date: 24/03/2020 12:51:51 ******/EXEC msdb.dbo.sp_add_alert @name=N'Error 825', @message_id=825, @severity=0, @enabled=1, @delay_between_responses=60, @include_event_description_in=1, @category_name=N'[Uncategorized]', @job_id=N'00000000-0000-0000-0000-000000000000'GO USE [msdb]GO /****** Object: Alert [Severity 016] Script Date: 24/03/2020 12:52:05 ******/EXEC msdb.dbo.sp_add_alert @name=N'Severity 016', @message_id=0, @severity=16, @enabled=1, @delay_between_responses=60, @include_event_description_in=1, @category_name=N'[Uncategorized]', @job_id=N'00000000-0000-0000-0000-000000000000' GO USE [msdb] GO /****** Object: Alert [Severity 017] Script Date: 24/03/2020 12:52:14 ******/ EXEC msdb.dbo.sp_add_alert @name=N'Severity 017', @message_id=0, @severity=17, @enabled=1, @delay_between_responses=60, @include_event_description_in=1, @category_name=N'[Uncategorized]', @job_id=N'00000000-0000-0000-0000-000000000000'GO USE [msdb]GO /****** Object: Alert [Severity 018] Script Date: 24/03/2020 12:52:22 ******/EXEC msdb.dbo.sp_add_alert @name=N'Severity 018', @message_id=0, @severity=18, @enabled=1, @delay_between_responses=60, @include_event_description_in=1, @category_name=N'[Uncategorized]', @job_id=N'00000000-0000-0000-0000-000000000000'GO USE [msdb]GO /****** Object: Alert [Severity 019] Script Date: 24/03/2020 12:52:34 ******/EXEC msdb.dbo.sp_add_alert @name=N'Severity 019', @message_id=0, @severity=19, @enabled=1, @delay_between_responses=60, @include_event_description_in=1, @category_name=N'[Uncategorized]', @job_id=N'00000000-0000-0000-0000-000000000000' GO USE [msdb] GO /****** Object: Alert [Severity 020] Script Date: 24/03/2020 12:52:44 ******/ EXEC msdb.dbo.sp_add_alert @name=N'Severity 020', @message_id=0, @severity=20, @enabled=1, @delay_between_responses=60, @include_event_description_in=1, @category_name=N'[Uncategorized]', @job_id=N'00000000-0000-0000-0000-000000000000'GO USE [msdb]GO /****** Object: Alert [Severity 021] Script Date: 24/03/2020 12:52:52 ******/EXEC msdb.dbo.sp_add_alert @name=N'Severity 021', @message_id=0, @severity=21, @enabled=1, @delay_between_responses=60, @include_event_description_in=1, @category_name=N'[Uncategorized]', @job_id=N'00000000-0000-0000-0000-000000000000'GO USE [msdb]GO /****** Object: Alert [Severity 022] Script Date: 24/03/2020 12:53:02 ******/EXEC msdb.dbo.sp_add_alert @name=N'Severity 022', @message_id=0, @severity=22, @enabled=1, @delay_between_responses=60, @include_event_description_in=1, @category_name=N'[Uncategorized]', @job_id=N'00000000-0000-0000-0000-000000000000' GO USE [msdb] GO /****** Object: Alert [Severity 023] Script Date: 24/03/2020 12:53:23 ******/ EXEC msdb.dbo.sp_add_alert @name=N'Severity 023', @message_id=0, @severity=23, @enabled=1, @delay_between_responses=60, @include_event_description_in=1, @category_name=N'[Uncategorized]', @job_id=N'00000000-0000-0000-0000-000000000000'GO USE [msdb]GO /****** Object: Alert [Severity 024] Script Date: 24/03/2020 12:53:32 ******/EXEC msdb.dbo.sp_add_alert @name=N'Severity 024', @message_id=0, @severity=24, @enabled=1, @delay_between_responses=60, @include_event_description_in=1, @category_name=N'[Uncategorized]', @job_id=N'00000000-0000-0000-0000-000000000000'GO USE [msdb]GO /****** Object: Alert [Severity 025] Script Date: 24/03/2020 12:53:52 ******/EXEC msdb.dbo.sp_add_alert @name=N'Severity 025', @message_id=0, @severity=25, @enabled=1, @delay_between_responses=60, @include_event_description_in=1, @category_name=N'[Uncategorized]', @job_id=N'00000000-0000-0000-0000-000000000000' GO