(Spoiler) I have some possible answer of what button means.

Eveybody knows that Marie (Max's wife) is the one who betrayed Rancel by giving the information to Spanish police and lured him into boarding that train. Then, Rancel was captured. Max tried to help Rancel by giving this green button as sign of either set-up or trouble, but it failed to be handed. Why did they use that green button to indicate that their secret identies of sending assigned propanganda from organization in exile to Madrid would be in danger?

By my understanding after having seen this movie, this green button belongs to Spanish-Police uniform because it is universally understood that, any token which belongs to both counterpart and enemy is a good guess as warning. Eventhough Max was not at railway station on the day of Rancel boarding that train, it is still possible that, if Max were there, he would have secretly handed Rancel this button there without any spoken word with him in order to avoid some possible surveillance by Spanish-police agents. And that would give Rancel a big clue to definitely stop getting on that train.

The last scene that Victor takes Max to railway station is because he wants his father to redeem the past memory he couldn't succeed in.