Ray Stantz encountered the Glutton while it was eating some tapes, record albums, and film reels on the second floor and attempted to stop it. Every time Ray took one away, the Glutton just took it back and ate it anyway. Infuriated by this, Ray attempted to charge at the ghost as it ate another tape, but it disappeared. It is unknown what happened to the Glutton, but it is likely that it was vented out of the Firehouse through the Containment Unit like the other ghosts.
Not much is known about the Glutton, but it appears to be so gluttonous, it'll just eat anything that isn't food. It is possible that the Glutton is even more gluttonous than Slimer.
As stated above, the Glutton will and can eat just about anything.