Tie the thyme sprigs together with kitchen twine; combine the pork, garlic, bay leaves and thyme bundle in a large Dutch oven. Add the vegetable oil, lime juice, orange juice, 1 cup water and 2 teaspoons salt and bring to a simmer over medium heat. Reduce the heat to low; cover and gently simmer, stirring occasionally, 1 hour.
Uncover the pot and continue simmering, stirring once or twice, until the pork is tender, about another 1 hour, 15 minutes. Increase the heat to medium; cook, stirring occasionally, until the liquid is mostly evaporated, about 35 more minutes. Discard the thyme bundle and bay leaves, then increase the heat to medium high so the pork starts to fry. Cook, stirring and scraping the bottom of the pot occasionally, until the pork is golden brown and crisp in spots, about 10 more minutes. Serve in tortillas with assorted toppings.
Pickled Red Onions
Combine 1 thinly sliced red onion, 1 cup cider vinegar, 1/2 cup water, 2 tablespoons sugar, 2 bay leaves, 1 teaspoon each coriander seeds, mustard seeds and cumin seeds, 1/2 teaspoon dried oregano and 1/4 teaspoon kosher salt in a small saucepan. Boil 2 minutes; let cool.