Anglo-Saxon pip, a pipe or flute.
Put that into your pipe and smoke it. Digest that, if you can. An expression used by one who has given an adversary a severe rebuke. The allusion is to the pipes of peace and war smoked by the American Indians.
Put your pipe out. Spoil your piping or singing; make you sing another tune, or in another key. “Take your shine out” has a similar force.
As you pipe, I must dance. I must accommodate myself to your wishes. To pipe your eye. To snivel; to cry.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894