Make the marinade - Place all of the ingredients for the marinade, except the cornstarch, in a small bowl, and whisk to combine.
Marinate the salmon - Add salmon to a medium sized dish, like a glass baking dish, and pour the marinade over the salmon pieces. Toss to coat, and gently press the salmon down to make sure it is covered by the marinade. Cover with plastic wrap and refrigerate for 3 - 4 hours.
Thread the skewers - Remove the salmon from the marinade, and gently pat dry. Thread the pieces onto skewers. (Do not overcrowd them. The pieces should not be tightly packed together.)On separate skewers, thread the pineapple, onions, and peppers. (It is ok for these to be packed a little tighter.)
Cook the teriyaki sauce - Add the marinade to a small pot and bring to a simmer over medium heat. Whisk cornstarch with 2 tbsp. of water and add to the simmering sauce. Let the sauce cook for about 10 minutes, until it is slightly thickened and glossy.
Heat - Preheat the grill to 400°F / 200°C. Fold a few layers of paper towel and dip it in oil, or drizzle oil on the paper towels. Holding it with tongs, run it lightly along the grill grates to coat.Leave one burner on the lowest heat, or no heat, so you can move skewers over as needed.
Grill the salmon - Place the salmon skewers and the pineapple/onion/pepper skewers on the grill. Cook for 4 - 5 minutes. Flip over, baste the skewers with the sauce, and cook for an additional 4 minutes. *Use the burner with low heat to hold skewers that are done, or those that need indirect heat to finish cooking through, without getting any more color on the outside (i.e. - burning).
Remove from the heat - Remove salmon skewers from the heat and let the fish rest for a couple of minutes before removing it from the skewers. Brush the salmon with sauce once more while it's resting. Serve salmon and grilled vegetables over rice, if desired.
Notes
Store leftover salmon in airtight container in the refrigerator for up to 3 days.