Hello! There are a few instances in the novel where Mameha talks to Chiyo about following orders. You can see that concerning matters of principle, the geisha world rarely references the word 'trust' directly. The principle of trust is alluded to, however. Arthur Golden attempts to paint a true picture of this Asian reticence in his novel; however, you will see that the 2005 movie actually has Mameha use the word 'trust.'
In the novel, when Mameha offers to take on the role of older sister to Chiyo, she tells Chiyo that her terms are very strict. She expects Chiyo to do as she is told without questioning or doubting Mameha's instructions. Furthermore, Chiyo must keep all communication between her and Mameha in utmost secrecy. Above all, Chiyo is not to relate any of the conversation that transpires between her and Mameha to Hatsumomo. Mameha's speech implies that she will only take on the heavy responsibilities of an older sister if Chiyo trusts her enough to do as she is told without second-guessing her older sister.
In another example in the novel, Mameha wants to orchestrate a bidding war for Chiyo's mizuage. The mizuage is when the highest bidder pays for the privilege of deflowering a virgin geisha. She tells Chiyo that the tall, thin cook is going to put a little cut on Chiyo's skin. At first, all the women present argue because they cannot decide whether to put the cut on Chiyo's leg or her neck, which is considered most erotic to Japanese men. In the meantime, Chiyo is getting nervous:
I felt like a slab of tuna the grocer had just delivered, because I could see now that I was the one who was going to do the bleeding.
In order to steady Chiyo's nerves, Mameha reminds Chiyo that she promised to always do as her older sister tells her. Again, the question of trust is alluded to. If Chiyo trusts Mameha, she should do as she is told. In the movie, when Mameha tells Chiyo she must make a cut on her leg, Chiyo is aghast.
Mameha: Now cut your leg where I've marked it.
Mameha: Or I will do it for you.
Chiyo: Have you gone mad?
Mameha: Do you trust me or don't you? Well? Go ahead, do it!
In the movie, Mameha warns Chiyo that she must do as she is told if she wants to demonstrate that she trusts Mameha implicitly, and also if she wants to secure her future. In the novel, Chiyo tells us that Dr. Crab paid 11,500 yen for Chiyo's mizuage, the highest sum in Gion and possibly any of the geisha districts at the time. This completely wipes out all of Chiyo's debts to the okiya. You can see why Mameha warns Chiyo that her trust must be implicit.
"Sayuri, we all have your best interests at heart."
Thanks for the question.