Any ideas on why the "turn on notifications for this gallery" is not appearing in the options widget?
The Media Gallery - Links widget provides a Subscription link only when rendered on the Media Gallery files directly and will only subscribe the accessing user to comments on that one file.
Here is a sample from my local instance:
If the intent is to subscribe to the actual gallery that is unfortunately not possible in any currently available version.
This feature, the ability for end users to subscribe to a Media Gallery to be notified on new files, has been added for v12.
That option, enables or disables new file notifications for Gallery owners only, not ordinary users. As a note, that has to be enabled in tandem with the option under Pencil > Manage Gallery > File Options that reads "Enable new file notifications for owners If enabled, owners of this media gallery will receive an email for each file uploaded to this media gallery."
Owners are listed under Pencil > Manage Gallery > Gallery Options: