At the character screen, click Change Quest.
Under ACT II Chapter 6: Betrayer of the Horadrim, select The Forgotten Ruins. Click Select Game.
Start the Game. Now walk to the New Tristram waypoint, and under Dahlgur Oasis, select Path to the Oasis.
You don’t have to walk the entire map in search of this item. Follow all the southern wall border up to the north east corner. There’s a small peninsula full of water that can appear up to three times throughout the wall border in a single map. Take a look at the mini-map below to see the shape of the peninsula.
The Mysterious Cave doesn’t have an icon on the map. It’s enabled and opened by an NPC. This NPC rarely appears in the Dahlgur Oasis. He is random. You should try running different games until the right random map appears. The NPC has no name at first. It’s easy to miss if you aren’t looking sharp. The screenshot below shows you how he looks like. He looks sick (sobbing position).
After killing the nearby demons, the NPC will stand up normal and a silver exclamation mark will hover above his head to talk to him.
After clicking him, you will now see his name. The NPC is named Zaven the Alchemist (Merchant). He says: “I meant to explore that cave over there for trinkets, but after that — it’s all yours.”
At that point, Zaven the Alchemist walks toward the sealed door behind him, and the Mysterious Cave becomes enabled. Check out if the merchant has something you like. He will have a different Rare (Yellow) item every time you manage to find this random NPC. Enter the Mysterious Cave.
The Mysterious Cave has two levels. What you are looking for is a chest named Mysterious Chest. There’s a catch, however. Zaven the Alchemist appears in a random Dahlgur Oasis map to enable the Mysterious Cave for you — but you won’t find a Mysterious Chest in all the random Mysterious Cave. It might require several trials. I ran about 10-15 Dahlgur Oasis maps. Zaven the Alchemist spawned two times, and only one had a Mysterious Chest. I’d consider myself lucky.
Inside the Mysterious Chest, you will — again — randomly find or not find a Liquid Rainbow.