Is it possible to assign an "hour type" to a template task?

Ideally, we would like project tasks to be automatically mapped to specific hour types based on the task, so that when someone goes to log their time in the task within a project, the hour type is already pre-selected - minimizing the risk that people choose the wrong hour type for that task.

I have tried creating a project with example tasks, assigning hour types to those tasks, and saving it as a template - but when I go to launch the template into a project, the task hour types default back to "Task Time" - which is not what was originally selected in the first project I created.

Thank you for any help on this one!