Here's an explanation of the "pinion":
An excerpt from Helmut Kühnhans, from "Die Uhr", No. 10, 1954 (German)
and an excerpt from Norbert Enders' essay "Zenith Calibre 135 - You watches on your bracelets, who has the biggest balance in all the land?":
...with the center wheel mentioned above - it is driven by the change wheel (direction of rotation!) - an additional transmission element had become necessary, which displeased Monsieur Jobin very much, because he wanted to transfer as much as possible of the precious energy of the mainspring barrel to the balance in order to obtain a powerful oscillation. Compared to the balance, the barrel is smaller than usual anyway - inner diameter 12.5 mm (picture 3).
Now, conventionally constructed small movements with crown winding afford themselves a certain luxury in terms of energy: the hand setting wheels always turn as well, driven by the change wheel. For reasons of stability, they are mounted on rather thick pivots - when setting the hands, the friction of the hollow drive on the shaft of the minute wheel has to be overcome - so some energy can be wasted.
Jobin put an end to this waste by using an ingenious device to establish the power flow between the change wheel and the following wheels only when it was necessary. For this purpose, the setting lever carries a pin on its underside that engages in a slot in a further lever mounted on a shaft below the setting lever. When the winding stem is in the normal position, the spoon-like end of the lever presses against the conical lower part of the second hand wheel, moving it upwards against the force of a leaf spring and thus out of the gear teeth of the change wheel . When the crown is pulled, the additional "spoon" lever moves away from the pointer setting wheel, which is pushed down by the leaf spring that engages in a groove of the hand setting wheel, and establishes the connection between the change wheel and the first hand setting wheel, which in turn is driven by the Rainure wheel (clutch drive). The shaft for the additional lever can be seen to the right of the minute wheel.
(Sorry - poor translation by me)
Kühnhans:
Nobert Enders' pics:
1. The spoon
Winding position
Setting position:
From above: