To prepare glaze: In small bowl, whisk ketchup, pineapple juice, brown sugar, soy sauce, garlic and ginger root until combined; reserve, refrigerated, for up to three days.
Heat grill to medium-high. Skewer ham, onion, bell pepper, pineapple and mushrooms by alternating pieces, and brush with about one-third of glaze. Grill 8-12 minutes, or until slightly charred and vegetables are cooked as desired, turning as needed.
Glaze skewers about halfway through cooking and again before serving. Garnish with green onion.