The peacock symbol is very common in the catacombs and in Byzantine Church art. Top is a fresco of "two peacocks and amphora in the tomb". Peacocks were often used in funerary art. Why?
The wonderful spread of the white peacock, originally from India is a wonder. Let's consider this variety of the peacock as one that has been "purified". It might seem like a silly idea at first glance, but surely you can find someone, somewhere, who has addressed this thought thoroughly and seriously in their writings.
A passage from one of today's Mass readings is on the subject of passing time and perhaps vanity as it applies to the allegorical peacock.
Ancient cultures revered the bird and there's a Greek myth about Hera to detail.
The suggestion that contemporary writer, Flannery O'Connor, could be added to the discussion is intriguing (and heady). She was deeply influenced by Søren Aabye Kierkegaard.
How the peacock (or peafowl) relates to all of this is another question. O'Connor writes about her strutting peacocks.
For early Christians
"the symbol of the peacock to represent immortality. This came from an ancient legend that the flesh of the peacock did not decay. It is also associated with the resurrection of Christ because it sheds it old feathers every year and grows, newer, brighter ones each year. If the peacock is portrayed drinking from a vase it symbolizes a Christian drinking the waters of eternal life. In addition the 'multitude of eyes' upon its stunningly beautiful fan tail, suggested the all seeing eye of God."