Thanks a lot Jeffrey !.
Yes, [NT SERVICE\SQLSERVERAGENT] login is there in the instance, however it was disabled.
The job works even when this account is disabled as well.
However when I dropped the login [NT SERVICE\SQLSERVERAGENT], started getting below error in error log.
Login failed for user '.....\test'. Reason: Token-based server access validation failed with an infrastructure error. Login lacks Connect SQL permission. [CLIENT: <local machine>]
When I remove "Sysadmin" privileges for the account, it just keeps running. Never completes.
So if I got it right,
When the job owner is a sysadmin in the instance, it runs under the service account set for SQL Server Agent.
However it doesn't matter whether that service account is a login in the instance or not OR what permission it has got, the job will always run under a special service SID account (NT SERVICE\SQLSERVERAGENT) which is sysadmin be default.
Hope my understanding is correct.
Thanks a lot !. Really helped to solve my issue.