Starting day 1, the HII should pop up sometime and no one knows who has them but if you click the HII along with dirt mounds you lose 5 health and you use it anytime until merge.
About the rocks, if the challenge immunity winner and the HII winner get the only eviction votes, the nonwinners pick rocks everyday and they're there just in case the votes happen and whoever gets white rock is eliminated.
This would increase the scattering of votes so rocks wouldn't have to be used.