I think he serves the same role as Kinshiki did to Momoshiki. They were partners, but Momoshiki was clearly the leader and Kinshiki acted more as a servant and guardian. I would say that this is in large inspired by the concept of "Sith" from Star Wars, as I would also argue that Madara and Obito's roles were inspired by Vader and Sideous from Star Wars. That the two work together and hold respect for each other, but they will always try to overcome the other, the apprentice will overtake the master.
In this scenario I would think that Jigen is actually the "master" of him and Kaguya, but at some point she tricked him and took the role as "master" from him. Believing Jigen to be dead she went on with her life and task and in the end died to her children. Jigen being still alive, but severely weakened hid his presence and plotted his return to power.