POST /api/v2/conversations/webchat/cobrowse returning 409 Conflict

Trying to kick off a cobrowse session from our Terraform-deployed backend. Sending a POST to /api/v2/conversations/webchat/{conversationId}/cobrowse with the correct sessionId in the payload. Getting a 409 Conflict back immediately. The conversation is active and the agent is already in the session. What am I missing?