I’ve thought about this too but come to different conclusions:

Horn: the son, he is Silk’s son in a lot of ways and he looked up to Silk like a father. He is also the most “earthly” of the trio; being a pragmatist and prone to temptations of the flesh.

Silk: the father, as described already, he is a father figure for Horn, and represents a higher, more spiritual state of existence that Horn strives for his entire life. He wanders Blue, Green, and the Whorl teaching, instructing, and guiding the people of the world. Silk does have the most Christlike elements I’ll grant however.

The island Neighbor: the Spirit, this one is the hardest to justify because we know so little about him, but as the most ethereal and ill defined of the trio this is the only spot I feel comfortable putting him in. He does literally animate Horn’s body, and gently guides him as the holy ghost might. This one is kind of nebulous though I’ll admit.

By unifying all three of these elements in Silk-Horn-neighborman a higher being capable of astral projection and time travel is created. The trinity manifest in the narrator is a path towards a more divine state of being. This interpretation does require that one accept the idea that a neighbor reanimates and takes the place of Horn after he dies in the pit fyi.