Verifying Cookie Persistence

How do you know for sure that the BIG-IP is using Cookie persistence and not Source persistence?

Because one is the primary and one is the secondary. This implies that the first will always be used unless it doesn't exist in the request. The cookie itself is an obfuscation of the pool-node-port of the selected member. You could then, technically, capture a known good cookie value for a pool member, create a new connection through a proxy-inspection product like Fiddler or Burp, and then swap the current cookie with the saved cookie. Assuming the above is true, the existence of this cookie should send the request to the new pool member, regardless of the secondary source persistence.