The tail of a fox or squirrel, which is brushy.
Brush away. Get along.
Brush off. Move on.
He brushed by me. He just touched me as he went quickly past. Hence also brush, a slight skirmish.
All these are metaphors from brushing with a brush.
Give it another brush. A little more attention; bestow a little more labour on it; return it to the file for a little more polish.
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Entry taken from Dictionary of Phrase and Fable, edited by the Rev. E. Cobham Brewer, LL.D. and revised in 1895.
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