Just love cooking Thanksgiving Turkey and just got a Traeger last year. Here is a recipe and method I have used for years cooking on my BGE. I usually cook about a 13 lb Turkey and spachcock it. I use an apple cider / honey / salt /acid brine I got from an Adam Perry Lang BBQ book "Serious BBQ"
Brine Recipe:
Use a food safe container to hold your bird. I use a tall square one intended to pack fish. Add enough cold out of the fridge apple cider to eventually cover the bird while retaining about a quart in a large sauce pan. Add 1 cup of Kosher salt, 1 cup of honey, and a bundle of fresh Simon and Garfunkel fresh herb sprigs to the cider in the sauce pan and heat until the salt and honey are completely dissolved. Spatchcock your bird. Mix the cooled cider / honey mixture with the cider in your container. Add 1 cup of cold orange juice, along with one orange thinly sliced and your herb bundle. Then add your bird, and let it sit in the fridge over night overnight, I usually go 24 hrs. It is important to keep the brine below 40 degrees during the whole process. I take a shelf out of my garage fridge and put my container in my fridge to insure it stays cold.
Cook:
The next day take the turkey out of the brine, wash it off and let it sit uncovered it the fridge for at least 2hrs prior to your cook. On my Egg I cook at between 350 and 375 allowing the temp to rise slowly during the cook. I pull my bird at an !T of 165 in the breast.
I tried to post a short video of last years turkey but it was too large for the site to take it, only pic I have. . I started using this method and recipe years and years ago, my family won't let me cook the Thanks Giving Turkey any other way. Ps. Towards the end of the cook I put some fresh rosemary sprigs on the grill around the bird and let them smoke and singe. Not a heavy smoke, more like a natural perfume essence. Cooking on your Traegers you can still use the brine and general method with some adaptation.