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More usually written as ‘Gang the same gait’. It means simply, “go the same way” in both the literal and figurative senses of the expression.
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“Gate” in Scottish is related to the Scandinavian “Gata”, meaning “Street”.
Further information from Bruce Herbold:
Milton Levy dance names (at least Abbot of Unreason as well as this one) draw on the writings of Sir Walter Scott. In The Heart of Mid Lothian a prisoner is bewailing his fate… "… in the book of Job: “He hath stripped me of my glory, and taken the crown from my head. He hath destroyed me on every side, and I am gone. And mine hope hath he removed like a tree.”
“Isna that ower true a doctrine?” said the prisoner “Isna my crown, my honour, removed? And what am I but a poor, wasted, wan-thriven tree, dug up by the roots, and flung out to waste in the highway, that man and beast may tread it under foot? I thought o’ the bonny bit them that our father rooted out o’ the yard last May, when it had a’ the flush o’ blossoms on it; and then it lay in the court till the beasts had trod them a’ to pieces wi’ their feet. I little thought, when I was wae for the bit silly green bush and its flowers, that I was to gang the same gate mysell.”