Steve, look carefully at the bizarre practices of states and individuals over the the past 800 years or so and you discover a really strange fact. Whether it be Napoleon, who wished to be seen as a Roman Emperor and cast in the role of Mars, or as far back as the ghastly costume designs of Inigo Jones who similarly accessed the Classical world, there is a tendency to look backwards. Now in doing so, there is also a marked leaning towards the Greeks and the Romans and their worlds. Strangely, the Romans emulated the Greeks of an earlier period whilst reviling the Geeks of their own time. Since then there have been three main Classical revivals, the first known as the Renaissance and the second in the 18th century courtesy of Messrs. Adams, Jones et al. The last one occurred in the late 19th century and seems to have been usurped by the Neo-Gothic revival which left its mark as late as the 1930s. So, the allusion to the votive cockerel could have been made during any of these 'fashions' or indeed maintained by a tradition of re-using motives in art?
By the way, cultural links going back over 2000 years are common for these and other more obvious reasons. You can't accept tradition in folk song and then say it doesn't happen in art.