The Record is one of the objects required to be placed in the pedestal room in order to fix the Ink Machine.
Exit the pedestal room, take the left hallway, and then the shorter left hallway. Turn right and enter the first door on the right. The Record is sitting underneath the table to the left.
Note that if you haven’t already, you can interact with the radio in order to obtain the achievement Crooner Tuner. There are also two Bacon Soup cans on the shelf on the right, if you’re interested in chowing down on them.
To get back to the pedestal room, turn left out the door, another left through the short hall, and then a right all the way to the end where the pedestal room is on the right side.
