Information about how to solve the hidden mechanism puzzle in Case 02: The Rabbit Hole - 2.2 - The Powers Club in Gotham Knights.
Near the beginning of 2.2 - The Powers Club you’ll have to dispatch two guards and scan near an indoor tree, where you’ll find a blood trail and a hidden mechanism beneath the floor. The means to activate this mechanism lie elsewhere, however, and while two wires will lead you in the right direction, they won’t lead you all the way.
Follow the wires up onto a balcony and through a door, and once through you can drop down to the left or right. Numerous guards patrol the area, and while there’s a bonus objective for solving this puzzle without being detected, if you’d rather focus on the puzzle, feel free to dispatch all the guards before searching for the mechanisms you need to interact with.
From the room beyond the balcony, turn left and drop down over a railing to find yourself in a larger room with several promising objects to scan. The piano and the statue of Athena are both duds, but the wire from the mechanism in the tree room leads to a bust, making this an easy enough mechanism to discover. Scan the bust, then interact with it. When you’re done, grapple back up to the room just beyond the balcony.
Jump off another railing, this time to the right, and you’ll find yourself in another large room crawling with guards. Once on the ground floor turn left and you’ll find some stairs at the end of the room. Head over to the stairs until you’re standing in front of them, then turn left to find some bookshelves built into the side of the stairs. Scan a book displayed on its side to find a hidden button, then interact with it.
Once both the button in the bust and in the book are pressed, return to the tree room and interact with the lamp built into a support pillar that powers the mechanical device under the floor. This will open up some stairs and allow you to proceed to the Owl Shadow Puzzle.