The Gear can be found in the same chest you’d taken a Dry Cell from at the start of Bendy and the Ink Machine.
Where can you find the Gear?
Exit the pedestal room and continue along the hall going to the left. Take the first short hall on the left and make another left toward the Ink Machine location, where you’ll need to jump over an ink pipe on the ground. This is the same area where you had to place in the two Dry Cells, and as I mentioned in that post, if you look in the chest to the left, there’s a Gear inside.
To get back to the pedestal room, take a right at the first hallway, then another right. The pedestal room is on the right side.
Place the gear on the pedestal to the far right.