Final answer:
Eli Katcher's role was that of a scrivener, where he handled legal documents due to an increase in work volume after his employer took on the 'master's office.' The job required efficiently producing extensive legal paperwork and involving a formal hiring process for additional staffers like Bartleby, described distinctively in the text.
Step-by-step explanation:
The role that Eli Katcher assumed upon employment was that of a scrivener, also known as a copyist or clerk, working in the legal field. His main duty involved the creation and handling of legal documents as mentioned in the text which refers to the work of a 'conveyancer and title hunter, and drawer-up of recondite documents of all sorts.' Katcher’s employer had recently taken on the 'master's office,' implying a significant increase in the volume of work related to legal documentation, thus necessitating more staff. The narrative also mentions the need to 'push the clerks already with me' indicating that Katcher's role would include a good amount of pressure to produce work efficiently. Additionally, the mention of receiving applications in response to an advertisement suggests a formal hiring process for additional positions such as the one Katcher filled. The character Bartleby who is described as 'pallidly neat, pitiably respectable, incurably forlorn' became one of the additional hires necessary to handle the increased workload.