Trace flag is running, but not message when deadlock happens
The reason the server wasn’t sending emails is due to this flag not being set:

EXEC master..sp_altermessage 1205, 'WITH_LOG', TRUE;
GO


Even though it was logging in the event log via the trace flag, this also needs to set in order to trigger the emails.
You can see the table here:

select * from master.sys.messages
where text like '%deadlock%'