The Desert Oasis Jewel's existence was revealed to Jack when looking deep into the Light of Eternity. It was revealed to Jack that the Jewel had great magic abilities. While it was not specified what kind of magic abilities it possessed the fortune teller who was the purveyor of the Light of Eternity assured Jack that it possessed the ability which he was looking for time travel. Though the fortune teller warned Jack that only someone who was pure of heart could use the power of the jewel.
Jack traveled through the desert with Ikra (Aku in disguise) and found the jewel. It was a large green gem floating above a small pool of water which was made green by the light of the gem. The Jewel tested Ikra and Jack and of course finding that Ikra was in fact Aku and evil it revealed the guardian of the jewel to be a large blue beast which fought fiercely but lost to Aku. The Jewel had placed itself on the forehead of the guardian. When the guardian lost Aku smashed the jewel on the ground revealing that he had only come along to ensure his failure.
It is likely that the jewel was restored after Jack destroyed the past Aku.