If it helps at all (bet it doesn't!), a "damper" is the thing in the flue of a fire that controls the strength of the draught. I suspect it moves a sliding plate somewhere.

Ah - Google has several listings under "push the damper in ", including this :

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Damper Song

Oh you push the damper in (thrust arm in with index finger pointing)
And you pull the damper out (pull it back)
And the smoke goes up the chimney just the same (point finger up with swirly motion)
Oh you push the damper in and you pull the damper out
And the smoke goes up the chimney just the same

Chorus

Star ar of the evening (point up)
Shining on the cookhouse door or or (slam the door)
Star ar of the ev e ning (point up)
And the smoke goes up the chimney just the same (point finger up with swirly motion)


Song is repeated several times in different styles for different versions. For example the Scout Leaders style (gut out) Guiders style (loud as you can) sex maniacs style (how do you push that damper in?) sissy boys version (guess), hippie style (hey man, like you push the damper in dude). Really, you can make it up yourself.
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