Bird going east and west (3)

I believe the answer is:

tit

I believe this is a double definition.

'bird' is the first definition.
(tit is a kind of bird)

'going east and west' is the second definition.

(Other definitions for tit that I've seen before include "Small garden bird" , "Small bird that lives off insects" , "18's [BIRD]" , "Boob made backing" , "useless horse, or not?" .)

I've seen this clue in The Times.

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