Re" I wondered what kind of instrument a waldvogelein was."

There is such an instrument. It is a kind of recorder, only 3 inches long and very high pitched. You play it by dipping the lower end in a stein of beer, then blowing and fingering in the normal fashion. The result sounds quite a bit like a starling in a lyrical mood.

I don't have one for sale, though.
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As for the song, I have decided that if the third verse makes sense, it does so in an awkward fashion. So be it.