It seems to have originated in the US with Fire Departments: > These reports show that a dry run in the jargon of the fire service at this period [1880s–1890s]

It seems to have originated in the US with Fire Departments: > These reports show that a dry run in the jargon of the fire service at this period [1880s–1890s] was one that didn’t involve the use of water, as opposed to a wet run that did. https://www.worldwidewords.org/qa/qa-dry1.htm https://www.worldwidewords.org/qa/qa-dry1.htm