I may be able to help on a few points, using experience from importing a Fulvia Sport 1,3S (1st series) to Switzerland.
1. It seems that in Italy at the time, flashing the lights using the button in the middle of the steering wheel was done on dipped beams. When the Swiss authorities tested a 1st series presented by the Swiss importer, they mentionned on the homologation paper that the headlight flasher needed to be modified to flash on full beam - see appended document (At the bottom of the page: Modifié par l'importateur: Avertisseur optique doit être branché sur les feux de route.). So I assume that in each country the importer modified the wiring to satisfy the applicable country laws. This may explain why we find such different operations on different cars! My Sport being an Italian car (from Pavia) we also had to change the wiring to flash on full beam! That function was tested during the 2022 technical inspection (very thorough!) and the car passed with no objections!
2. On my Fulvia too, the full beam of the headlights came with the lever pulled near the steering wheel, which was counterintuitive. When you check the operating manual, it clearly gives the other position for the main beams, i.e. the lever pushed away from the steeering wheel. We could not change the position by switching the wiring on the stalk, near the steering column. It had to be done by changing the wiring at the other end. It now works according to the operating manual!