Combine water, brown sugar, soy sauce, mirin, agave, garlic, and ginger in a saucepan over medium heat. Combine tapioca flour with 2 tablespoons water in a bowl; whisk until dissolved. Add mixture to the teriyaki sauce in the saucepan.

Heat sauce until it thickens to your desired thickness. Add more water if sauce becomes too thick.

Remove sauce from heat and reserve 1/4 cup for basting. Combine remaining sauce and chicken in a bowl and refrigerate for 1 hour.

Thread chicken strips onto skewers.

Preheat an outdoor grill for medium-high heat and lightly oil the grate. Grill chicken skewers on the preheated grill for 3 minutes per side, basting with reserved teriyaki sauce.