And it may be the motor does not need a capacitor but usually has a start switch, as mentioned previously.
If that is the case, once it is running, just having power across the blue and white would keep it going, with the other wires not connected now, only connected for starting.
Just another guess

oh right I forgot. I tried some before, I think it needs a start cap (it's why I came here)

OK, first things first. Remember that you are playing with line voltage. Getting across line voltage *can* cause injury or even death. If you are not using the series bulb (I'd recommend a 100W bulb at this point), then you may get an arc, and an arc creates ultraviolet light which can cause eye injury.

Leave the yellow and black disconnected. Apply line voltage to the white and blue wires. The motor should buzz loudly. Now momentarily connect the yellow wire to the blue and then then disconnect it again. Is the motor running? If so, note the direction and remove the power.

Now do it again, this time using the black wire instead of the yellow. Momentarily connect it to the blue wire to start the motor. Does it run in the opposite direction?

I understand, and that's why I'm not using a lamp. because I don't have a socket and don't have a safe way to connect it.
if you take a look at my setup, it has wirenuts and clamp connectors (for the capacitor) I even jammed in an old legacy power connector with stripped wires that way I can connect the motor safely (just gotta remember the colors of the wires are on the motor)

As for the disconnection I have a few spare light switches that I will try and use to connect and disconnect the capacitor safely.
thanks for the spark info though. I did have a situation where a spark came out of a motor because I connected it wrong. I will try to remember that.
I will setup the circuit in a moment.

 

Leave the yellow and black disconnected. Apply line voltage to the white and blue wires. The motor should buzz loudly. Now momentarily connect the yellow wire to the blue and then then disconnect it again. Is the motor running? If so, note the direction and remove the power.

Now do it again, this time using the black wire instead of the yellow. Momentarily connect it to the blue wire to start the motor. Does it run in the opposite direction?

I tried it, it worked! but it seemed to be scratching/running up against itself. also, the buzzing is pretty loud and it is a little concerning to have it running close to me. I still havent used it for longer that 3 seconds.

 

You should measure the current in the common power line with both cap in circuit and out of circuit , it may well be a permanent start cap motor.
i.e. left in circuit.
Max.