In a large food-safe container, such as a stock pot, combine the water, kosher salt, and brown sugar and stir with a long-handled wooden spoon until the salt and sugar crystals dissolve.
Squeeze three of the orange wedges and drop into the brine, reserving the remaining orange wedges. Add four of the onion wedges as well as the peppercorns, juniper berries, and bay leaves.
Remove any giblets from the main cavity of the goose as well as any large gobs of fat. Trim off any loose neck skin, or fold it over the neck cavity and pin it with a bamboo skewer or toothpick. Trim the first two joints off the wings. Wash the goose under cold running water and pat dry with paper towels.
Prick the goose all over with a sharp-tined fork or the tip of a paring knife, being careful to pierce just the skin and not the flesh. This helps the fat drain off during roasting. Submerge the goose in the brine and refrigerate for 24 hours.
When ready to cook, remove the goose from the brine and knock off any loose bits of aromatics. Discard the brine. Season the bird, inside and out, with salt and pepper. Tuck the reserved orange and onion wedges into the main cavity along with the apple wedges and the herbs. Loosely tie the legs together with butcher's string. Put the goose on a rack in a shallow roasting pan.
Start the Traeger grill on Smoke with the lid open until the fire is established (4 to 5 minutes). Set the temperature to 350F and preheat, lid closed, for 10 to 15 minutes.
Put the roasting pan with the goose on the grill grate and roast for 1 hour. Use a basting bulb to remove some of the fat from the pan. Save the fat for another use.
Roast for another hour; again, remove excess fat. Continue to roast the bird until the internal temperature of the thigh when read on an instant-read meat thermometer is 165F, 2-1/2 to 3 hours total. Let rest for 20 minutes before carving and serving.