Spray a loaf pan with nonstick cooking spray. Cover a brick or a heavy can from the pantry with aluminum foil; set both the loaf pan and the brick aside.
Combine the garlic and onion in the bowl of a food processor and process until both are finely chopped. Scrape into a colander or mesh strainer and let drain for 15 minutes, pressing on the solids. Do not wash the food processor bowl.
To the food processor bowl, add the ground beef, lamb, Traeger Souvlaki Rub, oregano, marjoram, and cayenne. Return the drained onion-garlic mixture to the bowl and process until a paste forms.
Press tightly into the prepared loaf pan. If desired, you can prepare the meat up to this point, then cover with plastic wrap and chill for several hours or even overnight.
When ready to cook, start the Traeger grill on Smoke with the lid open until the fire is established (4 to 5 minutes). Set the temperature to 325F and preheat, lid closed, for 10 to 15 minutes.
Bake the gyro meat in a water bath - this keeps it from getting crusty on the bottom - until the meat is 165F, 60 to 75 minutes.
Carefully remove from the water bath, drain and discard any accumulated fat, and set on a cooling rack.
Put the foil-covered brick on top of the meat to compress it. After 15 to 20 minutes, remove the meat from the loaf pan and thinly slice with an electric knife or a sharp serrated knife.
Build the gyros using the serving ingredients suggested above, finishing with tzatziki sauce.