In a small bowl, combine brown sugar, salt, paprika, chili powder, oregano, garlic powder, mustard, cayenne pepper, cumin and pepper. Season pork with brown sugar mixture.
Heat canola oil; working in two batches, add pork and cook until evenly browned, about 3-4 minutes.
Stir in chicken stock and 4 tablespoons vinegar, scraping any browned bits from the bottom of the pot. Select manual setting; adjust pressure to high, and set time for 40 minutes. When finished cooking, quick-release pressure according to manufacturer’s directions.
Remove pork shoulder from the Instant Pot® and shred the meat using two forks; stir in remaining 2 tablespoons vinegar and season with salt and pepper, to taste, if needed.