OK so in case you try Wireshark, I'm posting an trace of what connecting my 2 computers looks like. The zip file contains a .pcap file, which is a capture of the packets sent between the computers. Packet 99 in the capture starts the connection, as one computer (the client) looks for the server. There's some other packets from the internet in the middle which can be ignored. Basically there's communication between the computers around every 0.05 of a second, and most packets are quite short (5-100 bytes).
I also included (within the zip) an image of what the beginning of the trace looks like in Wireshark.