The term 'Jobs for a Gumshoe' refers to the occupation of a private investigator, also known as a PI or gumshoe. The crossword solution for this term is 'Cases, ' which refers to the cases that a PI investigates. Private investigators are hired to investigate a variety of cases, such as criminal investigations, missing persons, and corporate espionage. They use a variety of methods to uncover evidence, including surveillance, interviews, and research.