This is a "Wild Mass Guess" entry, where we pull out all the sanity stops on theorizing. The regular entry on this topic is elsewhere. Please see this programme note.
Elliot is actually Pete's deceased dad come back as his guardian angel.
Then the "other kid" could be another child of his. Or he realized now that Pete has a new family, he won't need him anymore and goes off to help other kids. It makes their good-bye that much more heartbreaking.
The next sequel (should it ever comes) will take place in the Present Day with another kid he's helping.