The term you're referring to, "guage," seems to be a common misspelling of the word "gauge." The correct spelling, "gauge," has an interesting etymology. It originates from the Old North French word "gaige," which means a pledge or a measure. This, in turn, came from the Frankish "*waddi" or "*wado," which is related to the concept of a pledge or a guarantee. Over time, the term evolved to be specifically associated with measuring instruments or standards, leading to its current usage in English.