The answer to this can be found on page 44 of my copy of Call It Courage. This is relatively early in Chapter 3 while Mafatu is exploring the island on which he has landed. He vows to Maui that he will return to his home island.
In this book, Maui is the god of fishermen. Maui is also the god that Mafatu honors most. We see him call to Maui a number of times. He prays to Maui when he is at some of his lowest points, such as on p. 86 when it seems that the wind has died and the cannibals will catch him. He attributes good things that happen to him to Maui’s intervention. For example, on p. 50 he gets the spear from the cannibals’ marae and believes that it was Maui who allowed him to do so without being harmed.
Because Mafatu honors Maui, it is to Maui that he makes his vow on p. 44. There he says
Maui, God of the Fishermen, hear me! … I shall return home one day, I swear it. My father, Tavana Nui, will be filled with pride at my homecoming. It is a vow that I take now, O Maui…
Thus, we can see that Mafatu’s vow is to return home and make his father proud.