I sing this myself from time to time and heard it from Johnny Collins. Perhaps he may remember. In his version the whole point of the "Fall Down" chorus is that in the song Billy falls off the yardarm and is killed.

The stitch through the nose line is possibly a clue as it was a tradition for a sailmaker sewing a corpse into a hammock for burial at sea to run a needle through the corpses nose (just to make sure!)

my $.02 worth