All is in pieces now.
It is thus easier to experiment for understanding how the internals work.
It has been the occasion to check that the damaged servo cable was still working (but repairing it will not hurt) and that the electronic board it as attached to works fine too. Not having a servo tester at hand, swapping servos and outputs was sufficient to check that all involved partners were ok.
That being said, the head is still not moving vertically, so something must be wrong inside (at the time of testing, I have not yet disassembled the robot as on the picture).
We open the head, after struggling a bit wit the bolt housing taps : use a small scalpel to lift a bit the rear part of the tap, so that you can then introduce a small screwdriver to act as a lever.
By zooming on the picture you can notice where the tool was used during the attempts.
For sure I will not install them back when re-assembling the head.
Once the head opened, we can see that there is a cable at the wrong place which hinders the moves of the involved servo. Aisoy’s assemblers were not that careful when producing my copy (I hope that I was just a bit unlucky)