Why does recaptcha have a distinct signature and if it does couldn't an attacker just make a distinct signature without recaptcha?
And why does recaptcha have a traffic signature that can distinguish between users? I mean how does a simple request response create a distinct traffic?
Or, my favorite, the binary search (assuming you control the server / the network in front of the server / some exit nodes, and can monitor the traffic of your targeted user): have sites that cause transmissions for some time (long running JS / requests, or just a lot of content the user interacts with). Freeze 50% of the servers connections. Is the user still connecting? Then s/he is in the 50%. If not, in the other. Repeat until the is user matched to activity on the server.
I'm not too sure about what defines the "distinctive" signature of recaptcha, but I expect timing of when packets of certain sizes were sent (e.g. loading 9 images in quick succession will generate larger packets, and then you often get the incremental couple images with human-length delays between them).