Hi all! Gotta love Google -- I was wondering about this song myself, and found the thread here. I had heard it from my grandmother, who's currently in her 80's. She had sung it in a barbershop quartet easily 20 years ago, and the typical tight harmonies of that style always come to mind when I hear the tune -- indeed the same melody as "Hold Your Hand Out, You Naughty Boy." When I got the chance I sent her an email asking for any information she could provide, recalling that I had seen it written as "Marianne." Here's what she had for me:

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The title is right. The song went as I rememmber it:

Pull your shades down Marianne
Pull your shades down Marianne
If you want to keep your secrets from your future man
Pull your shades down Marianne

She was combing her golden hair
Then she hung it upon a chair
If you want to keep your secrets from your future man
Pull your shades down Marianne

I was admiring her eyes of blue,
Then she took one of them out too,
If you want to keep your secrets from your future man
Pull your shades down Marianne

She was touching her pretty leg,
Then she hung it upon a peg,
If you want to keep your secrets from your future man
Pull your shades down Marianne

This was a song one of the barbershop group knew from her childhood, and she taught it to us. I am sure that I don't have all the small words correctly, but they are close. You might go on the internet and see if others my age remember? Hope this helps!
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Likewise, I hope this helps in terms of more verses; it's not much but she said she'd had a blast making it into a stage skit some time ago with all the various props for taking out the eye, removing the leg, etc. and a girl acting out the lyrics as they were sung, having a sharp backlight to cast a silhouette.