The tail of a fox or squirrel, which is brushy.
Get along. Brush off.
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.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894