There were car distribution clerks (large numbers of them at major yards) whose job was to track and locate available empty cars to fill agents/shippers requests according to car service rules and add them to switch lists for the yard switchers.
There was a recent Hindsight 2020 presentation on the work of a car distribution clerk at the joint UP GN NP SP&S Portland Terminal Railroad yard. Very interesting if you want to go into the detail of how railroads really operated before computers. There was a huge army of railroad clerks which produced the paperwork that kept American transportation working.
(Note I spent 3 years as member of The Brotherhood of Railway and Steamship Clerks, Freight Handlers, Express, and Station Employees union
at the very end before the computers took over completely in the early 1970's. If you can't lick em, join em.... I spent the next 42 years in Information Technology.)
Still in splendid Shelter In Place solitude, about half way up Walnut Creek