When are mature male wild boars typically observed joining the female-based sounders?

Only during the breeding season, referred to as the rut.

Mature male wild boars exhibit a predominantly solitary existence for the majority of the annual cycle, maintaining separation from the family units known as sounders. The sounders, consisting of related sows and their offspring, maintain a cohesive social structure led by an experienced female. The exception to this solitary rule occurs during the breeding period, which is specifically termed the rut. During this time, the adult boars will seek out the sounders to engage in mating activities. Upon arrival, dominant males must actively assert their status, often using aggressive displays, which can involve demonstrating the sharpness and size of their tusks, to establish access to receptive females within the group.