Soak 16 round, wooden toothpicks in water for 30 minutes. Whisk together olive oil, lemon juice, vinegar, sage and 1/2 tsp. each salt and pepper. Pour half into a separate bowl. Add chicken to one bowl and mushrooms to other. Toss; let sit for 30 minutes.
Remove chicken from marinade and season with 1 tsp. salt and pepper to taste. To make an "eyeball," place a cube of chicken on cutting board and push toothpick through. Push mushroom onto toothpick, cap side down; center carrot round on toothpick and push into indentation in mushroom to make "iris." Finally, center black olive half on toothpick and push onto carrot to make "pupil." Make 8 "eyeballs" this way. For other 8, omit carrot and black olive and push green olive half into indentation in mushroom. Discard chicken marinade; reserve mushroom marinade. ("Eyeballs" can be made up to this point and kept, covered, in refrigerator for up to 8 hours.)
Preheat broiler. Place "eyeballs" on a broiler pan. Position in oven so that chicken is 6 inches from heat source. Broil until chicken is cooked through, basting occasionally with mushroom marinade, 6 to 8 minutes. Arrange on a platter, in pairs, to look like a plate full of shifty eyes.