Running queries/jobs via SMSS - SQL service and SQL agent service accounts (SQL Server)
Job ownership is an important concept in SQL Server Agent. SQL Server Agent sets the security context for job execution based on the role of the user owning the job. 

By default, SQL Server Agent executes job steps under the SQL Server Agent service account irrespective of job ownership, or under the context of a proxy account. 
(about run as empty : Users who are not sysadmin have to access to the proxy account explicitly granted to their role or username)

The exception to this rule is T-SQL job steps, which execute under the security context of the job owner. 

If the job owner is a member of the sysadmin role, then the job step executes in the context of the SQL Server Agent service account. 

A common mistake when setting up jobs is to make "sa" the job owner – this will cause all T-SQL job steps to execute as the SQL Agent service account, which is a system administrator account. A better option is to set a non-sysadmin account as the job owner, and explicitly grant only the required database permissions to this account.

https://stackoverflow.com/questions/12112276/sql-agent-job-run-as-drop-down-list-is-empty

https://www.red-gate.com/simple-talk/sql/database-administration/setting-up-your-sql-server-agent-correctly/