What Triger Event of FME Automation to Chose When A Geodatabase Feature Class is been Updated

I think you should take a look at a similar question here: https://community.safe.com/s/question/0D54Q000080hFXDSA2/trigger-fme-workspace-when-arcsde-is-edited-by-separate-system

Essentially I think you would need to set up a database trigger. This is not my area of expertise but I think it will probably depend on the backend type of database (SQLServer etc) as to how to configure it. Here's a nice article which shows how to do this with SQL Server

https://community.safe.com/s/article/Single-edits-SQL-Server-Push-data-from-the-database-to-an-application-in-real-time