You would think that when you set the Submission Policy on a term set to be “Open” that this is all you have to do to allow users to add their own values to the term set from input forms.
After setting this parameter and testing the input form I was surprised to find that the option to add a new value was not present.
After scratching my head and searching around with google I found some information that led to the solution:
In the settings for the Managed Metadata column in the list there is a setting “Allow Fill-in” and this must be set to Yes to allow users to add values to the term set in the input form.
In hindsight, the configuration seems logical, but it definitely did not while trying to make it happen.