To button-hole a person. To bore one with conversation. The French have the same locution: Serrer le bouton [à quel quʹun].
“He went about button-holing and boring everyone.”—H. Kingsley: Mathilde.
To take one down a button-hole. To take one down a peg; to lower one’s conceit.
“Better mind yerselves, or Iʹll take ye down a button-hole lower.”—Mrs. B. Stowe: Uncle Tom’s Cabin, iv.