Cut each whole chicken in half, and set aside.
Stir together cumin, salt, and pepper in a small bowl.
Combine 4 teaspoons cumin mixture, olive oil, lime juice, and garlic in a shallow dish or large zip-top plastic freezer bag; reserve remaining cumin mixture. Add chicken to dish or bag; cover or seal, and chill 8 hours or up to 24 hours, turning occasionally.
Light one side of grill, heating to high heat (400° to 500°); leave the other side unlit. Remove chicken from marinade, discarding marinade. Pat dry with paper towels. Rub reserved cumin mixture over chicken. Arrange, skin side up, on unlit side of grill, and grill, covered with grill lid, 40 minutes or until meat thermometer inserted into thickest portion of thigh and breast registers 150°.
Brush chicken with Guava Glaze. Grill, covered with grill lid, 30 more minutes or until meat thermometer inserted into thickest portion of thigh registers 180° and thickest portion of breast registers 170°, brushing every 10 minutes with glaze. Cut chicken halves in half between breast and thigh to make 8 serving-size pieces.
*Substitute 4 bone-in, skin-on chicken breasts and 4 chicken leg quarters, if desired.