I'm referring to "secure flow" and not "secure pause". Secure flow is an inbound flow that can be used to collect sensitive data and allows the call to be returned to the same agent.
Sorry about that, read too quickly. I've opened API-2990 to expose the /api/v2/conversations/{conversationId}/participants/{participantId}/secureivrsessions APIs publicly. I've submitted the change, but it may not make it to prod until after the holidays. Keep an eye on the conversation API docs for this resource to show up.