Place wood skewers in a container of water and let soak to prevent burning while you prepare the recipe. You can use metal skewers instead if you prefer.
In a medium bowl whisk together tamari or soy sauce, rice vinegar, coconut sugar, sesame oil, garlic, and ginger. Divide in half, setting half aside for the teriyaki glaze and using half for the marinade.
Place chicken and half of the sauce together in a bowl with a lid or a tightly sealing plastic bag (reusable bags work great). Let marinade on the counter top for half an hour while you prepare the sauce. If preparing for later, let marinade in the refrigerator for up to 24 hours, removing half hour before cook time to allow the meat to come to room temperature.
While chicken is marinading, add remaining reserved sauce to a small sauce pan over medium-low heat and bring to a simmer.
While sauce is heating, whisk arrowroot and water together until dissolved (use the bowl that the sauce was in to minimize dishes). Pour into the saucepan.
Add 2 teaspoons honey to sauce as well an let cook for a few more minutes until sauce has lightly thickened. Remove from burner and set aside while cooking chicken.
Preheat your grill and clean and oil the grill grates. Or, you can cook on an indoor electric grill, in an oiled skillet, the oven, air fryer or however you prefer (see notes).
While grill is heating, remove skewers from water and pat dry. Skewer chicken pieces onto the skewers.
Grill the chicken skewers over high heat, rotating every few minutes until they are beginning to brown and chicken is cooked through (8-10 minutes depending on grill temperature)
Immediately place the chicken skewers on the serving plate and use a grill brush to baste the teriyaki glaze evenly over each skewer.
Sprinkle with green onion and sesame seeds and serve immediately.