Can I report on the duration/time a tag was on a ticket?
Unfortunately, there is no way to report on events of tags. This means that reporting on the time or duration that a tag was on a ticket is not possible. However, if the tag was applied because it was associated with a drop down or check box field, then you can report on the amount of time a field value was selected. This setup will require creation of multiple custom metrics, the logic is explained here: Duration between two or more ticket events in minutes.
For more information on tag reporting, see Insights tag reporting: Reporting on tickets with one or more tags (Professional and Enterprise).