Field not available on template editor when creating a new template
User does not have write access to the field OR there might be a "save_as_template" ACL on the table the template is for, which the users do not pass.
Create save_as_template ACL on the affected table. The ACL can be specific to one field or a wildcard to allow all fields in the table to be available in templates.
For more information on save_as_template ACL please use below link for our documentation on this.