Just so you know, the "chicken teriyaki sauce" in a bottle does not taste like real teriyaki sauce in Japan. Teriyaki is a cooking technique. "Teri" means the "luster" given by the sweet soy sauce marinade and "yaki" means "cooking or grilling," and it’s not really the name of the sauce.
Prick the chicken on the flesh side with a fork.
Combine the soy sauce, water, mirin, sugar, onion, ginger, and 1 tablespoon of the sake in a bowl or zip-lock bag. Add the chicken, place in the refrigerator, and marinate for 2-3 hours.
When ready to cook, heat 2 tablespoons of the vegetable oil in a large skillet over medium-high heat. When hot, shake off as much marinade as possible from the chicken and place the chicken pieces skin side down. (The marinade will burn easily so try not to add any of the liquid to the pan. Do not throw away the marinade.)
When it's nicely browned, flip and cook the other side. Then, add the sake and cook, covered, for 8-10 minutes. Remove the chicken to a plate and clean the skillet. Heat the remaining oil over medium-high heat and put the chicken back in the skillet, skin side down first to make the skin crispy. Then, flip again and pour in the marinade. Cook until the sauce is reduced a bit. Baste the chicken a couple of times while cooking. Serve the chicken and pour the sauce on top.