Combine 1 tablespoon oil, white wine vinegar, and next 3 ingredients in a large zip-top plastic bag; add squash. Seal and turn to coat. Let stand 2 hours.
Remove squash from marinade, reserving marinade. Brush squash with remaining tablespoon oil.
Cook acorn squash, covered with grill lid, over medium-hot coals (350° to 400°) about 10 minutes on each side. Place on a serving dish; drizzle with reserved marinade. Cover squash, and let stand 10 minutes. Garnish, if desired.