The proper name for the Time Cave reputation is the Time Keeper Reputation. You can first grind to the Cave of Time entrance and the Time manager to the quest Master's Nest followed by the Cave of Time Light, the old Hillsblad, Talessa's stratagem, escape Dunhold, return to Andorm, the Black Swamp, open the dark Gate, the Dragon hero.
Then it's time to paint a replica of the old Hillsbride Hills and Black Marshes.