Actually, the peacock's tail is not a mystery, it was only Darwin's cultural bias that made it seem so.

Gaudy and expensive (in biological terms) sexual displays are evidence of excellent fit of the population to the environment and the resulting surplus of energy available to the population members.

The Peahen, who is much more plain, can fly and roost in the forest, limiting her risks from predators. The Peacock has that advantage as well, and both are large enough to limit the kind of predator that can pose a risk. With their flight abilities, both can easily harvest a bounty of food, enough to support both their large size and in the males, extravagant sexual display feathers.

Once the cascade of sexual selection based on feather display begins, it will only be limited by resource richness and predator vulnerability...the peacock's tail is the literal evidence of the relative weakness of predator risk or resource poverty.