Mix banana ketchup, lime soda, lemon juice, soy sauce, white vinegar, brown sugar, garlic, kosher salt, and pepper in a bowl. Add the sliced chicken thighs, cover, and marinate for at least two hours in the refrigerator.
When chicken is done marinating, thread the meat through the skewers, leaving about 3-4 inches on one side. Set the skewers on a plate or sheet pan.
Reduce the leftover marinade in a small pot over medium-high heat. In the meantime, light your grill (gas) or fire your coals to get them hot.
Spray the grate with oil and grill chicken skewers over hot coals using direct heat (about 4 inches away) for about three minutes on one side. Turn over the other side and baste with the reduced marinade. Grill for another three minutes while frequently turning and basting to ensure the chicken is evenly cooked on both sides. It usually takes about 8-12 minutes to cook depending on how hot your grilling surface is.
Transfer the chicken to a serving plate and serve with warm rice and atchara (Filipino green papaya relish), cucumber, and tomato slices.