Heat the oil in a large heavy pan or Dutch oven, and brown the chicken pieces until lightly golden on all sides, about 10 minutes. Transfer the chicken to a bowl.
In the same dutch oven, whisk the water, brown sugar, 3/4 cup of fruit juice cocktail, soy sauce, ketchup, bourbon liqueur, apple cider vinegar, garlic, dried onion, red pepper flakes, and ground ginger into the Dutch oven. Bring the sauce to a boil while scraping the browned bits of food off of the bottom of the pan with a wooden spoon.
Stir the chicken back into the sauce, and bring to a full boil over medium-high heat. Reduce the heat to medium-low, and simmer until the sauce is reduced and thickened and the chicken pieces are no longer pink in the middle, about 20 minutes.
Remove the chicken pieces to a bowl with a slotted spoon. Stir together 1/4 cup of fruit juice cocktail with the cornstarch until smooth, and whisk the cornstarch mixture into the sauce, stirring constantly to avoid lumps. Bring the sauce back to a simmer, let thicken for about 1 minute, and return the chicken pieces to the sauce. Stir to combine, and serve.