What did Timothy teach Philip in Theodore Taylor's The Cay?

In Theodore Taylor's young reader's novel The Cay, Timothy teaches Phillip many things including the value of self-sacrifice, independence, and perseverance. Two teachings that keep Phillip alive the most are independence and perseverance.

When Phillip becomes blind due to a severe head injury, he feels completely vulnerable and dependent. Timothy teaches him that he is actually very capable, despite his blindness. Though Phillip resists learning at first, the more he realizes Timothy is trying to help him be independent, the more willing he becomes. Through Timothy's help, Phillip learns how to weave sleeping mats, build a shelter, build a device to catch rain water, make his way around the island using a cane, and fish. The more independent Phillip grows, the braver and stronger he becomes until one day he decides he is able to climb the coconut tree in order to harvest the coconuts for their nutritious meat and milk. At one point, while climbing the tree, he freezes from fear, but though Timothy comforts him by saying, "'Tis no shame" to come back down, Phillip persists because he can't bear to disappoint Timothy (p. 99). Phillip succeeds in climbing to the top and in dropping coconuts to the ground, a very significant and symbolic triumph.

By the time Timothy sadly passes away as a consequence of weathering the severe hurricane, Phillip is able to continue taking care of himself. Most importantly, though he is all alone at this point of the story, he has learned not to feel defeated. When he is alone and a plane flies overhead without landing, though he sobs at first, he has gained enough inner strength from Timothy to be able to calm his emotions down and think rationally about what might have caused the problem and how to fix it. He figures out that the smoke coming from the signal fire must have been white, which would be impossible for a plane to see. He further figures out that adding the oily sea grapes to the fire might turn the smoke black. His black smoke signal soon works, and he is soon rescued. However, if Timothy had not taught him perseverance, he would have succumbed to a fate of death on the island.