PATCH /api/v2/conversations/calls/{id}/participants returns 409

Trying to drop a specific participant from a conference call via PATCH /api/v2/conversations/calls/{id}/participants. Sending a payload with {"state": "not-participating"} for the target ID.

Getting a 409 Conflict back. The docs say this should work for active participants, but the response body is empty. Anyone else hit this wall?