It could be better document, but Tasks API allows specifying timeout param

https://www.elastic.co/guide/en/elasticsearch/reference/current/tasks.html

The task API can also be used to wait for completion of a particular task. The following call will block for 10 seconds or until the task with id oTUltX4IQMOUUVeiohTt8A:12345 is completed.
GET _tasks/oTUltX4IQMOUUVeiohTt8A:12345?wait_for_completion=true&timeout=10s