Our Gemara on Amud Aleph discusses the impact of the Godol Habayis, the principal member of the family, on the shiva process. The Shiva is not just observed by an individual, but rather the family observed Shiva. Thus, when Shiva starts or ends may depend on when the Godol Habayis is present. The definition of Godol Habayis seems to depend less on age, and rather on role and leadership.
Shulkhan Arukh YD 375:2 codified it as follows:
Those who send a corpse to another large town for burial and they know not when he [the corpse] will be buried, as soon as the mourners turn their faces to come back from escorting the corpse, they begin to count the seven and thirty days of mourning and commence the observance of mourning rites. On the other hand, Those who accompany the corpse, count the days of mourning from the time that he is buried. However, if the chief of the family accompanies the corpse, even those who remain here, count shivah only from the time he is buried. The chief of the family means the one upon whom the household depends and who are guided by him, irrespective whether he is a brother or a young son. However, there is one authority who says that he must be [at least] thirteen years old.
Kitzur Shulkhan Arukh (240:9) defines the role further as the person who would assume leadership and decision making in regard to the burial process.
Regardless, we see from the poskim that family roles and leadership do not always follow typical age or gender roles, as families tend to arrange themselves according to internal patterns. Which brings me to a discussion about healthy and unhealthy roles in families. A family role is a set of behaviors and responsibilities that is consciously or unconsciously placed upon a family member that allows for the material and emotional maintenance of the family. Like in an individual, when the roles are healthy they maintain optimum function and growth, but when they are defending against uncomfortable thoughts and feelings, they often maintain a rigid, stagnant function with little growth.
Some examples of unhealthy family roles include:
- Hero: A child who is successful in ways that please his or her parents. Sometimes later in life, this catches up to them with feelings of emptiness, because the achievement was not intrinsically motivated.
- Scapegoat or Troublemaker: Challenges the family’s written and unwritten rules. This role is kind of like a suicide mission; it can either break the denial and cause change or end up literally or figuratively killing everyone. Think of the child who becomes an addict or goes OTD.
- Lost child: The child who doesn’t make waves and is kind of ignored. May not be an academic achiever but since he or she is quiet and doesn’t make trouble, gets socially promoted. This too may backfire later in life with feelings of emptiness and depression, as there had not been much ownership of life decisions.
- Mascot: The cute one, maybe the baby or youngest who entertains everyone and distracts from the dysfunction and conflict. This can either make for an adult with high social skills, possibly a person in the entertaining or hospitality kind of industry. Indeed many comedians tell of stories of their dysfunctional childhoods and how they resorted to humor to break the tension. However the danger also can be a feeling of worthlessness and depression because not enough self care was developed. Think of Robin Williams who committed suicide.
- Caretaker: This is the child who helps the parents physically or financially. Sometimes the dependence is so great that the child never gets married, or if married, the spouse feels as if the parent is more of a spouse than he or she is.
Source:
https://journals.sagepub.com/doi/full/10.1177/1066480720973418
Some Examples of Healthy Roles include:
- Provider of Resources: This person provides the financial resources for the family.
- Nurturer: This person tends to the emotional needs of family members. In this case, I am referring to normal, healthy functions such as love, care, empathy. This is different than codependence where aside from nurturing and taking care, the nurturer feels compelled out of guilt and fear and often is chasing people down to accept the nurturance, or forgiving and enabling selfish or self-destructive behaviors.
- Life Skills Developer: Someone who offers practical guidance and wisdom to family members.
- Manager of the System: The person who makes sure the bills are paid, medical appointments kept and other maintenance. As with the nurturer role, it should come out of normal needs, and not fear, anxiety or guilt. An obsessive person can over manage in a compulsive, intrusive manner.
Source
https://vtechworks.lib.vt.edu/bitstream/handle/10919/48301/350-093_pdf.pdf?sequence=1&isAllowed=y
Roles should be relatively balanced, fair, and open to negotiation. It is not unusual for one member or the other to be a flag bearer on a particular set of skills and it is not necessarily dysfunctional. In successful marriages and relationships, there often is an uneven distribution of responsibility and talents. It does not have to be equal. The main thing is that it works well, and feels motivated out of love and mutual respect for various skills and weaknesses, without it feeling coerced or compulsive.
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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