Call him the Chinese version of God. He's everywhere and nowhere, he's the creator of all Earth, and he knows how to use his powers.
For example, when the Monkey King tries to prove that Tze-Yo-Tzuh does not have "'all of existence—forever […] within the reach of [his] hand'" and that the Monkey King can "'escape [Tze-Yo-Tzuh's] reach'" (4.59), Tze-Yo-Tzuh completely handles him.
How, you ask?
He lets Monkey fly all the way "past the edges of the universe" (4.66) and "through the boundaries of reality itself (4.67) until Monkey reaches five pillars of gold. Monkey goes ahead and tags one of the pillars with what amounts to "The Great Sage Equal of Heaven was here" in Chinese (4.49-4.70), and then he pees on the pillar he tags (4.70). Totally satisfied with himself, Monkey flies back to Tze-Yo-Tzuh, only to find out that those five golden pillars were actually the fingers of Tze-Yo-Tzuh's left hand (4.75-4.77).
Now that's a neat trick.
Tze-Yo-Tzuh's more than just the ultimate trickster though—he's also the character who drives Monkey forward toward Monkey's ultimate transformation into a humble, good monkey. He's the one who first buries Monkey under a mountain of rock (4.90-4.96), then second sends Monkey his chance at freedom and redemption through self-love in the form of the monk, Wong Lao-Tsai (there's a write-up about Wong Lai-Tsao elsewhere in this section that you might want to check out).
And that's important because Monkey is the one to mobilize Jin toward his final transformation into a guy who learns to love his Chinese self.
So Tze-Yo-Tzuh really is the force behind every major character in the book, even if he operates through the power of other characters.