Task.await tries to exit the calling process when the timeout hits, but IEx traps the exit in that process, so it doesn't terminate and thus the linked task process doesn't either, I think? If I do all of this wrapped in another task, rather than directly in IEx, then I observe the innermost process get terminated by the process link after the intervening one doesn't trap the exit.

Relevant from https://hexdocs.pm/elixir/1.4.5/Task.html, which you've probably already seen:

> If the timeout is exceeded, await will exit; however, the task will continue to run. When the calling process exits, its exit signal will terminate the task if it is not trapping exits.