Ok so i talked to our resident machinist at work (he does really cool shit like converting a 3axis CNC into 5Axis mill at home) and asked him about the motor. Bluegill and our Resident Machinist had the same Idea. that the motor wasn't wired for 110V and that's why it flicks on and off. however i opened up the motor to tried to wire it to low voltage diagram Which i assume is 115v. However the guy who wired this up originally didn't wire it up anywhere close to the diagram and i have no idea how to wire it up right as the original diagram is super hard to read and i don't understand the terminology. Like t5 or t10, I have wired a 3d Printer before so it isn't my first rodeo wiring but i have no idea how to wire up this motor correctly. that's where smart people like you come in, i need help wiring the motor and the diagram is hard to understand for my very smol hamster brain like mine.
so from what i understand. this my recreation of all the diagrams also im glad i took it apart because the drive pully for the motor i could slide off with my hand and one of the terminals wiggled inside the motor.
as-well as pictures of the original wiring and board
If any terminals wiggle that couple be a sign of something broken internally. I have seen motors where low voltage as 220V, and high voltage was 440V - they were 3 phase, so probably not what you are looking at, but there is a possibility that your motor can't run on 110v)
At this point you are beyond what I can help you with on the internet. Maybe i could see something obvious if I looked in person, but probably stuck finding someone who can come visit in person to see what you are missing.
The terminal wiggles but its because the nut was loose on the top of the screw. I have tightened the nut and it no longer wobbles since I tightened the screw.
I just dont think a wobbly screw would give the motor such a problem but that's why I mentioned it. I dont think the reason my motor would flick on and off is because of the loose terminal.