It's strange- their focus is the maintenance of the world, but they were created and manipulated to want nothing more than to be with their gods- or fathers- whatever framing it makes it easier to understand.
Which makes one wonder the truer nature of the fal'Cie. Are they independent lives created from parts of their parents, and yet also part of their parents - that at the end, they would reunite with their parents, in that they would return to the mind that they are actually from? Or are they separate beings created from parts of their parents, so that when all is said and done, they will still be with their parents at the end, but separate lives at the same time? I hope this makes sense, but I'm not sure I know a way right now to make better sense of it.
From what it sounds like, Pulse and Lindzei are like the over-soul in which their respective fal'Cie children will return to. The power, the mind, everything will be absorbed back into Pulse and Lindzei respectively. And then, further more, when done, Pulse and Lindzei will be reabsorbed into Bhunivelze. In Lightning's chapter in Fragments After, she - and hence we - are told that Bhunivelze divided his power to create all three of the fal'Cie. Then, the fal'Cie Pulse and Lindzei did the same to create the 'lesser' fal'Cie. It sounds as if the power that is Pulse and Lindzei has its own mind, but is a part of Bhunivelze, and then the 'lesser' fal'Cie are from the same power, ultimately, but from Pulse or Lindzei respectively.
Unless I am wrong, perhaps like Jenova cells, the parts wish to be reunited and part of the whole again?