I'm the long time owner/user of a 4/200-400 VR I (got mine in I think 2006) and used it extensively for years shooting surf, and since I don't do that any longer, nowadays for shooting catwalk, initially on a D2X, then on a D3 when that became available, and nowadays on D800's
Don't own a D500, so don't have in depth experience with the improved MultiCam 20K AF
Recently played with a D850, in particularly tried my hand with the AF, but that was too short to be able to make a serious evaluation of it.
Did seem an impressive improvement over the CAM 3500 AF module in the D3/D800 though, despite the short time I was able to experiment with it
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Don't recognize the jittery AF issue you describe, but must say that based on the description it doesn't seem be a related to the AFS motor itself problem; agree with the suggestion it might simply be a matter of dirty contacts
That said, given the high number of AF points of the Multicam 20K AF module, might it be a consequence of the camera having, as a consequence of the selected number of AF points (as in the f1 Custom Control Assignment setting) ?
Even with the the lower AF points Cam 3500 AF module, in certain situations and with certain settings, using all 51 points can confuse the camera and cause somewhat erratic AF behaviour/jumping around
Have run into a 'jittery image' problem with this lens in the past.
Turned out that was due to a faltering VR motor, the consequence of years of shooting surf in the rain while constantly being covered with salt water spray without any kind of (rain) cover for lens nor camera.
In the end some of that salt water got inside the lens and corroded the electric contacts of the VR motor inside the lens, making it jump rather then move fluently while stabilizing the lens elements concerned
Got 'fixed' when NPS repair disassembled the lens for a repair estimate and, after I declined the repair, reassembled it, in the process cleaning those contacts
On a side note, as someone who has used/uses the lens most of the time for shooting subjects moving (fast) in sometimes erratic patterns
I do wonder why you use back button focus when shooting what appears to be static subjects, even if at varying distances
I personally always keep the AF on the release button, use the AF back button to 'pre focus' in anticipation of a shot I think I might take to shorten the 'reaction' time for the lens to focus when I do take the shot
Or in situations, as described in another reaction, where eg due to atmospheric conditions combined with far away subjects, the camera might have a problem finding a point to focus on, or the AF of the camera is put under more pressure due to use of a TC
my two cents