That appears to be a button, not a trackball.
From pg. 17 in a presentation, Active Stick & Throttle for F-35 - Joseph Krumenacker - NAVAIR Flight Controls / JSF Vehicle Systems - 16 October 2008, found here:
It is used to engage/disengage stick sensitivity in hover. Inadvertent movement of the stick would disengage the altitude hold.
Engaging that S-5 ...
They move, pretty much like an F-16 stick.
From this MIT lecture "F-22 Flight Controls", Lt Col Randy Gordon, F-22 test pilot (from the transcript):
It's a side stick.
Initially it didn't move.
Eventually they decided, I'll put in some deflection.
So I can go a half inch left, a half inch right, about a quarter inch
forward, I go about a half inch ...