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Basically the Gym is under a Museum. To reach the Leader you have to gather pieces of fossils scattered in the caves under the Museum, then match each with the proper habitat to continue to the Leader. If you fail you battle a trainer with some random rock mons (Geodudes, Boldores, etc.) and the fossil mon whose habitat that one belongs to. (You can also just go to them and battle after finishing the test if you want to.) After beating one you get a short description of the Fossil Pokemon and the niche it once held.
If you get through 5 (Maybe less or more depending on which Gym number it's supposed to be) such rooms you reach the Gym Leader, Gene. He claims to have unlocked the true potential of Fossil Pokemon through his relentless study into archeology and genetics.
Each of his mon know a Signature Move they don't normally learn.
After defeating him he gives you the Primeval Badge and a TM for a Rock Move. If you bring him your Fossil Mon, he can Tutor them so they learn a Signature Move.
Ex: Omastar - Whirling Shot - Water/Special/90 BP/90 Accuracy/If the user used a Status Move last turn, this move gains +1 priority.