There is a scientific source that claims equal succession existed, it just wasn't practiced by the nobility because the nobility was NOT Basque.
Just because the title of the book is something like "in the 19th century", the specific claim is still clearly about medieval times. There are also sources disputing it
I've had access to the article of Arrizabalaga. The topic of the article is the changes in succession in the 19th century, she mentions that during the previous centuries (at least since the 16th century) that equal succession was practiced but doesn't go deep into it or how of by who was practiced. She just mentions it as some sort of context to the topic of her article.
Nobles are well documented. Even in times where it could be reasonably claimed that they were Basque or at least native to the contemporary Basque Country and Navarra (Arista and Jimena Dynasties in Navarra, and the house of Vasconia (768-1032)) they definetly did not practice Equal Succession as can be seen by analyzing the holders of the titles and their familes. Is worth noting that there is no Female title holder ever for this earlier period, in fact the first female holders are in the XIII century, and because they had no surviving Male brothers.
There is no doubt however, that women had considerable power (when compared to other European regions at the time). Found this, for example:
http://euskararenjatorria.net/wp-content/uploads/2013/06/R.M.Frank_._Basque_Law_Code_Papers1.pdf
In fact the text you quote confirms that Male preference was the norm
Art. I indicates that in noble homes the eldest male had precedence over the elder female child.
There you have it.
However, in the next article (Art. II), the privilege of masculinity is rejected in favor of the rule of primogeniture: "Mais s'il y a enfants de divers mariages, et du premier n'y a que filles, la fille aînée du premier mariage succède et exclut tous les enfants des autres mariages, posé qu'il y en ait de mâles."
And this refers to another situation where the owner of the house has children from different marriages. It actually says that "IF ONLY has daughters from the first marriage (the one that has a better right to succession) then the eldest daughter of that first marriage should inherit".
It must be noted that all property acquired via marriage was deemed right of conquest in the Navarrese Law, so if you didn't give each son of the previous marriage their part when one of the spouses died they could claim rights to the property you got via the second marriage by right of conquest.
The name of the text is "The Remarkable Role of Women in 16th Century French Basque Law Codes ", but of course these laws in the 16th century weren't created in a vacuum, they were based on older Basque traditions.
That may be so. However, it was not unheard of for new things to be added in 16th century Codification and make them pass as if they were "immemorial custom" so we have to take what is said there with a grain of salt. For example, in the
Fuero Nuevo of Biscay of 1526 all naturals of Biscay are set to be noblemen, while nothing of it is in the
Old Fuero and certainly wasn't the case for the previous centuries.
Still, all of those customs refer to peasant families and property, not to nobility (the characters represented in the game). This "primogeniture" thing started as a way to avoid the partition that peasants were supposed to do (Primogeniture was a Monopoly of nobility) by granting all the property in the Marriage Contracts as a dowry to the couple you wanted to get the property while the parents still were living and by making the young couple commit to take care of those parents, who now were not the owners of house and property. More than a succession law it was a Marriage Dowry custom to avoid the actual inheritance law.
It is also known that this "Equal Primogeniture" was practiced only in the French part of the Basque Country (which isn't even represented as Basque in the game) and not in Navarre or the Spanish Basque Country (which is represented as Basque in game).
So in other words, it's not really clear how it was handled, but it seems clear that at least allowing them to chose equal succession from early on seems perfectly reasonable.
No it is not, at least not for the AI, because right now what we have in the game is a Kingdom of Navarre and Duchy of Vasconia that always follows Equal Succession despite those states clearly not practicing that kind of succession ever in their History. Navarrese Medieval History is my area of expertise and sources are quite clear on this topic.
However, to have Equal succession as an option available just for the Human player is completely fine, but as long as the AI stays historical.