MySQL 5.6 Bug Amazon RDS with replica. AFTER INSERT TRIGGER is not working. Solutions?
According Paragraphs 1-3 of MySQL Documentation Replication and Triggers


  With statement-based replication, triggers executed on the master also execute on the slave. With row-based replication, triggers executed on the master do not execute on the slave. Instead, the row changes on the master resulting from trigger execution are replicated and applied on the slave.
  
  This behavior is by design. If under row-based replication the slave applied the triggers as well as the row changes caused by them, the changes would in effect be applied twice on the slave, leading to different data on the master and the slave.
  
  If you want triggers to execute on both the master and the slave—perhaps because you have different triggers on the master and slave—you must use statement-based replication. However, to enable slave-side triggers, it is not necessary to use statement-based replication exclusively. It is sufficient to switch to statement-based replication only for those statements where you want this effect, and to use row-based replication the rest of the time.


MySQL default for binlog_format in 5.6 is STATEMENT and ROW in 5.7. You will have to set that in the DB Parameter Group. You may need to convert the binlog_format to STATEMENT on RDS Master, RDS Slave, and the External Slave. Only the can you configure a trigger on the External Slave.

Interestingly, MariaDB has in its Documentation Running Triggers on the Slave for Row-based Events. You may have to switch to MariaDB.