You don't get new clues until the normal game time for rods to repop. If you were able to gather the Sienna and Amber, you will begin getting clues for them once the in game timer for gathering them wears off. That is a long time. As an example, I'm not 100% but I am fairly certain that you could use all 4 charges of the amber back to back and you would still have to wait a while for a new amber to come up and it has the longest duration.