Recently I got TombstonedTaskError and I would like to know what is the duration for the TombstonedTaskError?
TombstonedTaskError is raised if you're attempting to enqueue a named task using a name that has been used recently, see What is TombstonedTaskError from App Engine's Task Queue?.
The duration of the de-duplication logic has been documented since that answer was posted. From Naming a task (emphasis mine):
When you create a new task, App Engine assigns the task a unique name by default. However, you can assign your own name to a task by using the name parameter. An advantage of assigning your own task names is that named tasks are de-duplicated, which means you can use task names to guarantee that a task is only added once. De-duplication continues for 9 days after the task is completed or deleted.