OK, caught up, sort of.
This rather took me by surprise, my suspicion that it was a simple fault was right, but not being familiar with this ball head it threw me for a moment.
The faults were two fold, firstly the body of the retainer sleeve for the rotation lock was loose, it should have been tight. Secondly the rotation locking knob had been unscrewed over-strongly which had unscrewed the body of the retainer sleeve from the main ball head body. I wasn't sure how it worked at first, not wishing to damage anything I approached it gingerly. Eventually I gripped the retainer body in a pair of pliers and applied some force, Yea! the knob came loose in it's retainer. Job done! Almost.
I extracted the reamed screw, identified the thread as M3 x 0.5mm pitch. I rummaged through my boxes of screws and found some stainless steel Torx screws which I had salvaged from one of my Mac computers. It was my liquid cooled G5 Tower, these screws secured the logic board to it's mountings and are really nice quality. However, they were cheese head, not countersunk. Off out to the lathe, eventually found some aluminium bar, drilled and threaded it M3 and screwed one of the screws I had found into the end of the bar, tightened it then cut a countersink at 45º so the screw fitted perfectly. Then I did two more, these replaced the other two original screws. They need a TX8 driver.
The three other screws accessible through the hole in the rotating base must be left well alone... They are special screws which are designed to tighten but not unscrew. They have a clever 'one way' clutch design which allows the screws to be driven in but not unscrewed without either special tools or destroying them by grinding or cutting the heads off.
Some pix...
The rotation lock screw and housing, in the unlocked position, as I found it, unscrewed tightly and jammed:
The rotation lock screw and housing, in the locked position, achieved by screwing the knob in:
The lathe, set up with aluminium bar in the chuck:
Close up of the screw:
And from the back:
These pix were taken with my D3300 and my rough, workshop 18-105 VR lens.
I propose to apply some thread lock to the rotation lock screw housing threads to prevent the housing coming loose again in the future. I may apply a tiny amount to one of the rotation plate screws too. One, the one which reamed had had thread lock applied. If anybody thinks it would be better not to apply Locktite please tell me, these screws are small and could ream again with Locktite applied.
Your thoughts David?