A reel motor is the motor inside a VCR or tape recorder that drives the reels, it's just a small DC motor. They all look different to each other, depending on the manufacturer - you should be able to get one from an old VCR.
However, finding one EXACTLY the same as used in the project would require knowing what make and model it came from.
**broken link removed****broken link removed** **broken link removed****broken link removed** **broken link removed****broken link removed** **broken link removed****broken link removed** https://electronics.howstuffworks.com/motor2.htm