How is a T-SQL Trigger that only fires on real changes made?
You can handle both INSERT and UPDATE with an EXCEPT set operator.
The EXISTS will only evaluate to TRUE both if it's just an INSERT, or if it's an UPDATE with different values for any of these columns.

IF EXISTS (
           SELECT First_Name, Last_Name, JobCoe, Inactive FROM inserted
           EXCEPT
           SELECT First_Name, Last_Name, JobCoe, Inactive FROM deleted
          )
BEGIN...