Yet again we salute the sailors of old for today’s saying.
When, in the eighteenth century, the government put import taxes up on various items such as tea and spirits to such levels that ordinary folk simply couldn’t afford them, it led to a boom in smuggling. This in turn led to an increase in the size and vigilance of the Revenue Service, whose cutters prowled the coasts trying to intercept contraband. They were allowed to board incoming vessels and search them, and one of the main hidden items they tended to find was rum. Hence, the phrase came into being that they were performing a rummage as they searched the ship.