Timothy gave Phillip faith that what two things would happen?

Timothy gave Phillip faith that they would be rescued and that Phillip would be cured of his blindness.

Even while on the raft, Timothy repeatedly assured Phillip that a boat or plane would come by to rescue them. Days would go by with no rescue, and Timothy would still insist that a particular day would be the day of rescue, that their luck was good, with the implication that they would not die on...

Timothy gave Phillip faith that they would be rescued and that Phillip would be cured of his blindness.

Even while on the raft, Timothy repeatedly assured Phillip that a boat or plane would come by to rescue them. Days would go by with no rescue, and Timothy would still insist that a particular day would be the day of rescue, that their luck was good, with the implication that they would not die on the raft. Once on the island, Timothy made plans to build a signal fire and to arrange a message consisting of the word "help" where it could be seen from planes flying above. While Phillip might have succumbed to despair from their situation and from his blindness, Timothy reminded Phillip again and again that rescue was imminent.

He also assured Phillip that his vision would return. On the day that Phillip went blind, on the raft, Timothy seemed to invent a story about a friend of his who had gone temporarily blind, but then began to see again after a few days. This calms Phillip down and gives him hope that his blindness is only temporary. But when his sight doesn't return soon, Phillip is terrified and asks Timothy to tell him again about his friend who had lost and regained his sight. This time, Timothy's lie is more obvious: he changes his story and says it had taken his friend much longer than three days to get his vision back. Regardless of whether Timothy is lying, he's giving Phillip some measure of hope and reassurance about the boy's eyesight.

Interestingly, Timothy is right on both accounts: Phillip gets rescued, and his sight is restored. But even if neither of those things had happened, the hope that Timothy gave Phillip kept him alive, and kept him from sinking into despair, throughout their time on the raft and on the island together.