[intakexhaust]

^During the ride, I missed seeing him do it but apparently the process goes something like this:

Open axle release lever.
Axle has teeth which ride on the teeth in the dropouts. Its precise enough to keep all in alignment.
When axle release is loose, you pedal slightly forward to relax chain tension.
The other lever moves a fork set over the top of the chain. Select cog by moving that lever.
Once in the desired cog, tighten axle with the other lever.
I would guess the process is easier going from low range to high gear. The wheel when loose would naturally guide rearward.

Probably not unlike gingerly shifting a vintage Ferrari. Do it wrong and its mayhem.

Other: If you noticed the pic of Bartali he also has a front rod shifter. I have one like that yet for rear derailleur with usual spring tension - works fast and efficient. But used in combination Cambio Corsa and with changing front rings, you have to make up the slack too! That means all the mickey mouse rear lever action at the same time... yikes.