The set quoted above was recorded by Peter Kennedy and Mervyn Plunkett from George Spicer of Copthorne, Sussex, in 1956. (Folksongs of Britain and Ireland, 1975)

Laws 09; Roud number 1437

Entry at  The Traditional Ballad Index:
Branded Lambs [Laws O9]

The song has often been found in the South of England, most usually as Searching for Young Lambs, and P.W. Joyce published a short (four-verse) Limerick set of the same title. It has also been found occasionally in Canada and in Scotland .  A connection to the better known (though far less common) Searching for Lambs (Roud number 576) has been suggested at times, but the majority opinion seems to be that there is little or no relationship.

George Spicer can be heard singing Long and Wishing Eye on  As I Roved Out: Songs of Courtship (Folktracks FTX 013)

I take it that we'll be getting the tune?