A person who is pervicacious resists other people’s suggestions or advice, determined to do things their own way. In other words, a pervicacious person is stubborn or obstinate.
We have several more ordinary words for this character trait, including headstrong, bullheaded, pigheaded, and willful. Pervicacious is a sophisticated alternative; it's so uncommon that a stubborn person might not even realize they're being insulted if you use it to describe them. The word comes from the Latin pervicax, meaning "stubborn." The prefix per- means "thoroughly," and the root vic- comes from the Latin verb for "to conquer." A pervicacious person thoroughly conquers any opposing ideas by simply refusing to give in.