Het Masteen doesn't have a tale. For all we know he might have a tail (he never takes off that robe), but we doubt it. The Consul does let us know that Masteen is the captain of the treeship Yggdrasil (a giant flying space tree. Really.) and he's also the True Voice of the Tree. We're not sure what that is, but it sounds important. Aside from that weird old grandma tree in Disney's Pocahontas (and, well, the ents), trees don't talk, so it's nice that they have a representative or some sort.
Anyway, Masteen is serious and quiet. The one time he makes a joke (and it's not that funny), the Consul notes that it's, "the first sign in all [his] decades of dealing with the Templars that one of them had shown even a nascent sense of humor" (1.70). They may not be funny, but they do love nature. The Tree Templars follow the teachings of The Muir, who may or may not be John Muir, the founder of the Sierra Club.
This religion is still kind of a mystery to us. We only know Masteen's view on the Shrike: "While many Templars believe that the Shrike is the Avatar of punishment for those who do not feed from the root, I must consider this a heresy not founded in the Covenant or the writings of Muir" (1.80).
After Sol Weintraub tells his tale, the pilgrims stand on the deck of the windwagon and watch the sky. They see not just stars; they see the Yggdrasil get shot down by the Ousters, crash and burn. Masteen says nothing, just goes inside in ominous silence.
The next morning, Masteen is gone, and his room is splattered with gore. Either someone murdered him and dumped the body, or he exploded out of sheer sadness over that tree. We're not sure which, and the pilgrims don't know either. Lamia remarks, "We don't know a damn thing except that Captain Masteen isn't in his room and a lot of blood is" (5.17).
Well, it turns out we were all wrong. Somehow, Masteen's not only okay, but he's going to reach the Time Tombs ahead of everyone else. While in Chronos Keep, the final stop on the pilgrimage, they see Masteen out the window. At least, they see someone dressed like him, and who else would wear that? "The figure was tall and robed, its back to the Keep, and strode across the flashing vermilion sands with purposeful intent" (6.85).
How ironic that Het Masteen, the one we know the least about, may just reach the Time Tombs first. Maybe he's the only one who actually has true faith.