What are some things that Timothy taught Phillip?

Even before Timothy realizes that his illness is serious, and that he'd better prepare Phillip to live alone on the island, blindness and all, the kind old man has begun to teach him things of value.

First, notice how he teaches Phillip to make the sleeping mats out of the palm fronds. Sure, the sleeping mats are useful, but the more important thing that Timothy is teaching the boy is that he has the capacity to work and get things done even though he lost his vision. Phillip keeps trying to get out of doing the work, keeps trying to make Timothy think he's as helpless as he feels. "The hands aren’t blind though," Timothy replies. This assertion instills in Phillip the belief that he has the power to survive.

Next, let's look at what Timothy teaches Phillip after the old man's illness has become serious. In Chapter 13, he teaches the boy how to fish, saying quite reasonably, "Well, you mus' den know how to provite your own self wid feesh." With patience and a soothing voice, Timothy teaches Phillip this invaluable skill and even helps him learn what to do if he falls into the water--something that Phillip is terrified of, ever since falling from the raft.

Later in Chapter 13, Timothy gives Phillip encouragement and help as the boy learns to scale trees to cut down coconuts. This is not just a practical survival skill but also a lesson in perseverance to the young boy: the fact that he previously couldn't climb the tree really bothered Phillip, but now that Timothy taught him successfully how to do it, they feel that "D'palm harass [them] no more." Meaning, of course, that they've conquered the impossible. Phillip feels so accomplished and so happy from eating the coconuts that he even thinks:

"It was almost as if I'd graduated from the survival course that Timothy had been putting me through since we had landed on the cay."

That "survival course" continues as Timothy teaches Phillip how to prepare for a hurricane in Chapter 14, how to tie down supplies and find high ground. As he's learning this from Timothy, Phillip realizes that he's also been taught how to conserve resources:

"I realized then why he had used our rope sparingly; why he had made my guideline down to east beach from vines instead of rope."

Because Timothy has taught all of these practical and psychological survival skills to Phillip, the old man's sad passing doesn't mean that Phillip is helpless afterward. Yes, Phillip is a child, and yes, he's blind, and totally alone on the cay, but Timothy's lessons keep Phillip alive until he is finally rescued.