The song that I called a volkslied is in fact a poem by Joseph von Eichendorf (1812) with a melody by Glück. On closer inspection, it is not really a broken token song, as the broken ring is a symbol of broken faith, rather than the token of enduring faith. The parting in
Das gebrochene ringlein is permanent.

"the miller's lovely daughter was standing at the door, reflected in the water, I saw her face once more; reflected in the water, I saw her face once more." fits Gluck's tune, and includes a Miller's Daughter, but is not a translation of any verse in the poem (at least as far as included in the Allgemeines Deutsches Kommersbuch.) My unsupported guess is that Gilbran's song is a softer paraphrase, suitable for young people, inspired by Eichendorf's harsh original.