When using the API, is it possible to Notify the Customer when Note is added to an Incident?

When I add a comment to an incident via the API, I would like to be able to notify the customer attached to the incident of that fact. I am already able to notify the customer when the incident itself is updated, but notes do not seem to share this functionality.

Here is an example of the API call I am trying to make:

'curl -u x:<MY_API_TOKEN> -H "Content-Type: application/json" -d '{"comment":{"parent_id":"5290","type":"comment","note":"Here is my response"}}' https://deskapi.gotoassist.com/v1/incidents/5290/comments.json?note_type...(link is external)'

Interestingly, if I add a comment via the web GUI, the notification DOES go to the Customer just as I want.