Tough one without being able to feel the headset as its turned.
I tighten the nut until i feel binding then back it off slightly until it moves freely, then the rock test i cup around the bottom cup and top of fork to feel for play, only rock gently and feel the play in your hand, there is play in the brakes too which can transmit itself through the bike, one way to eliminate this to some degree is to turn the bars 45deg so the wheel is pointing sideways and the brakes cant rock back and forth, feel for the play in the actual cup. If you can do that and feel a slight knocking, and it will be slight, and tightening it up a smidge creates binding, then something in the headset is either missing worn or wrong.
Just for reference, here is all the original parts of your headset: