The Golden Vase can be found inside a cave in the Vikings (831 AD) time period of Time Tangled Island.
To get it, go in front of the cave with the entrance blocked by a bunch of rocks. Click on the rocks to use your Gunpowder. The entrance will be cleared. Once you enter, you'll have about 30 seconds inside the cave to find the golden vase: it's in the bottom left corner. Use the map to find it. If your fire extinguishes before you can reach the vase, you will return to the cave entrance, and you will have to try again.
When you return it to the oracle on the hill in Ancient Greece (328 BC), that time period will be restored.