The mail agent only runs when it has emails to process, you can see that here:

select * from msdb.dbo.sysmail_log

You can then check emails that were sent here:

select * from msdb.dbo.sysmail_mailitems

There are other mail tables that can be queried for profiles etc.

You can also check that database mail is enabled with this:

sp_configure 'Database Mail XPs'