Yep. If the client gives up its full list of currently cached intermediate certificates it certainly reveals information about its connection history. Clients w

Yep. If the client gives up its full list of currently cached intermediate certificates it certainly reveals information about its connection history. Clients would probably need to use per-site certificate caching. But in general your point about fingerprinting is well made. The more negotiation that happens between the client and server, the more data that is available for client fingerprinting and tracking from the server side.