Well when you acquire one of the fossils in the desert the other fossil you didn't choose will appear in mirage tower so it can be either the root fossil or claw fossil.
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In Pokémon Emerald, Mirage Tower will appear in the Desert that is to the North of Mauville City however it will only appear once you have spoken to the Ruin Maniac in Fallarbor Town. Once you head into the Mirage Tower, you will need to use the Bike that is the Mach Spike because of the various sensitive cracks in the floors. However once you have picked 1 of the Fossils then it (the Mirage Tower) will disappear and it will not return at all.
The top floor contains two fossils. To get to the top, a Mach Bike and Rock Smash are required. Wild Sand shrew and Trapinch can be found in the tower.
In Pokemon Emerald, both the Root and Claw fossils can be obtained. One may be selected at Mirage Tower and the other will be found at the end of the Desert Underpass.
You need mach bike
Mirage Tower is in the desert around the enterance near Mauville. It only appears every once in awhile. I'm not sure how often though.