How to send a notification to On-Call contacts via the API

I've gotton POST Notifications working for single contacts (broadcastContacts.externalIds and .contactIDs) and for an entire group (broadcastContacts.groupIds). I would like to send a notification to only the currently on-call person in a particular group. The group has a linked calendar and a staffed shift. It also has sequencing enabled.

What is the correct combination of broadcastContacts and broadcastSettings to achieve this?