The work or profession of being a detective or private investigator; detective work or surveillance.
From 'gumshoe' plus the gerund suffix '-ing', which converts a noun (the detective) into describing the action or profession itself.
Notice how English lets the same word become a verb ('I was gumshoeing around town') and a noun ('Gumshoing is tough work')—this flexibility is one reason English is so popular for slang and colorful descriptions!
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