Prepare a hot fire in a charcoal or gas grill. Or heat a large nonstick skillet over high heat. Brush the cooking surface with oil. Cook the meat in batches (leave the onions in the bowl, or most of them—it’s fine if some of the onions stick to the meat), taking care not to overcrowd the grill or pan, turning the meat once, for 3 to 5 minutes per side, until it is cooked through and has a nice char all over the surface. As you cook, transfer the cooked meat to a lidded container, or transfer to a platter and cover tightly with foil.
If using a grill, use a vegetable grill pan to cook the onions. Grill the onions, turning with tongs, until tender and lightly browned, about 5 minutes. Or cook the onions in the skillet. Scrape the cooked onions over the meat.
Slice the meat into approximately 1-x-1⁄4-inch strips. As you cut it, return it to the covered container so it stays warm.
Heat a comal or large skillet over medium-low heat. Working in batches, heat the pita bread or tortillas, turning once, until warmed through and lightly browned on both sides. Wrap the first batches in a clean kitchen towel to keep warm, or use a tortilla warmer.
To assemble the tacos, arrange a generous amount of meat and onions on the middle of or inside each pita bread or tortilla (the traditional way is to top the pitas as if they were tortillas). Top with the salsa, drizzle on the tahini sauce, and serve.