Can you share the personal story from the text that illustrates how Sai encourages a devotee's good intentions?

Certainly. Chapter 19 recounts a personal experience where the narrator decided on a Wednesday night to undertake continuous chanting of Rama's name. Upon waking the next morning, the name of Rama was naturally present in his heart. After making a firm resolve and completing his morning ablutions, he set out for Sai's darshan. The moment he stepped out of Buti's Wada, he was greeted by the sound of Aurangabadkar singing a beautiful, sweet song. This was interpreted as Sai's immediate and encouraging "gift of grace," a confirmation of the devotee's pious resolve that was delivered without the Guru even moving his lips, showcasing the marvels of Sai's skill.