Combine vodka, cinnamon, allspice, and cloves in a bowl. Combine 1/2 cup vinegar, soy sauce, hot sauce, and garlic in another bowl. Cover both bowls and allow mixtures to rest for 8 to 10 hours at room temperature. Strain vodka mixture and discard spices.
Press tomatoes through a sieve to make 1 cup tomato pulp; save any excess tomato pulp for another use.
Heat 6 tablespoons vinegar and sugar in a skillet over medium heat, stirring constantly, until mixture is deep brown and syrupy, 6 to 8 minutes. Stir in tomato pulp and reduce heat to medium-low; simmer until thickened, 4 to 6 minutes. Remove and discard garlic from soy sauce mixture and pour sauce into tomato mixture. Bring to a boil and stir in tamarind pulp and strained vodka. Continue to cook until sauce is thickened, 10 to 15 minutes.