This can be any number of things from the motor to the collar. You will really need to look deeply into what may look bad. Encoder/housing or gearbox are mostly likely however.
That said, it is doing this at home because it's trying to see the change from the high side of the collar and the low side and back. This quick, short movement is the only time you see this.
Things to check:
1. Gearbox - can you push the arms easily by hand? I've seen them be able to push them all the way closed
2. Is there a lot of up and down slop on the arm? This can be bearings
3. Is the collar rusted/broken/damaged? This is what the BF prox sees
4. separate the motor/gearbox. How does the motor key look? how about the encoder gear?
5. Is there oil leaking out of the gearbox? when you try to turn the gearbox from the input shaft is there a little bit where it doesnt turn?
6. Do you have the old gray colored encoder housing or the e-coat black? If gray, they corrode and crush encoders easily.
FWIW Id put my money on gearbox. I'd get that, the shaft, bearings, collar, hardware at least though. I'd be surprised if it came apart as easily as you're hoping and it's easier to replace the bearings with that all apart.
Good luck