SQL Server Agent/Properties/Alert System/Mail Session/Test is disabled
Test button referred in the question is only available for older version of SQL Servers that supported SQL Mail. Below picture is from a SQL2008 SP4 instance where you can use the test button.



From books online:


  SQL Mail is not installed by default in SQL Server. For more
  information, see Understanding Surface Area Configuration. SQL Mail is
  not supported on 64-bit versions of SQL Server. SQL Mail stored
  procedures cannot be installed on 64-bit versions.


For Database mail you can use this feature for testing.

Using SSMS, Instnace-->Management-->Database Mail-->Right click-->Sent test Email.