Answer
Check the Application Messages window — every time a Send Email-type event action executes, it creates an Application Message (by default in the NOTIFICATION queue), and if that message ends up in a Failed state, opening it shows a detailed error explaining exactly what went wrong (for example, one confirmed case failed with 'Mail address 'To' field is not specified,' meaning the recipient value the event action was supposed to supply came through empty — a missing/empty recipient rather than a Mail Sender configuration problem). Application Messages is the general place to check whenever a custom event/event action appears to have silently not worked, not just for email specifically.