Green’s Dictionary of Slang

to stop bragging or boasting.

1920		Marvel 29 May 3: Turn off the gas and pay up!
1922		(con. 1918–19) S.V. Benét Beginning of Wisdom 296: ‘Oh, turn off the alarm-clock,’ he gasped.
1937		E. Raymond Marsh 274: Turn that tap off, Mr. Huckstead. That’d go down all right up west, but we know better here.
1964		L. Hansberry Sign in Sidney Brustein’s Window in Three Negro Plays (1969) I ii: Turn off, Fag Face!