Interesting story. Tait and Tate are both found as spellings of this surname. It comes from the Old Norse teitr, meaning "cheerful", but it seems to have been a given name rather than a description. I think it belonged mainly to Northern England and Lowland Scotland. Tait was the name of a Scottish Border clan, based in Roxburghshire, and Tate and Lyle are a well-known firm (sugar refiners) based in Liverpool.