A gender-neutral euphemism for masturbation - flexibly encompassing solo, mutual, and partner performance fellatio.
This phrase is dually used to outline a power dynamic. That is to say, obediently walking a peacock not in your charge implies passivity and an absence of individual agency whereas having one's peacock walked symbolizes dominance.
Tanya's carpal tunnel interfered with her menage a moi so she called up Josh to walk the peacock.