Bring 4 cups of water to a boil in a 4-quart saucepan. Add the wild rice and a generous pinch of salt, reduce the heat to maintain a gentle simmer, and cook until tender, 30 to 45 minutes.
Meanwhile, heat the oil in a 12-inch skillet over medium heat. Add the sausage and cook, breaking up any big chunks with a spoon, until browned and cooked through, 3 to 4 minutes. With a slotted spoon, transfer the sausage to a paper-towel-lined plate. Add the onion and 1/2 tsp. salt to the skillet and cook, stirring occasionally, until just tender, about 3 minutes. Add the vermouth and with a wooden spoon scrape up any browned bits from the pan; cook until the vermouth evaporates, 1 to 2 minutes. Add the sage, thyme, and bay leaves (if using), and continue cooking until the onion is very tender and the herbs are fragrant, 3 to 4 minutes. Return the sausage to the pan, add the pears, and cook just until warmed through, 1 to 2 minutes. Remove from the heat and set aside.
In an 8-inch nonstick skillet, melt the butter over medium heat. Add the pecans and cook, stirring often, until lightly toasted, 1 to 2 minutes. Add the brown sugar and stir until melted and beginning to caramelize, 1 to 2 minutes. Sprinkle with a pinch of sea salt, transfer to a plate, and let cool. Roughly chop the nuts.
When the wild rice is cooked, drain any excess water. Return the rice to the pan and cook over medium heat to dry out slightly, 1 to 2 minutes. Remove the bay leaves (if used) from the pear mixture. Add the pear mixture to the wild rice and toss to combine. Season to taste with sea salt and pepper. Transfer to a serving bowl, sprinkle with the chopped nuts, and serve.