Basically what the above says, assuming the eavesdropper must be completely passive, and cannot connect to the server to check if the server requires a client certificate.
TLS handshake protocol in brief:
All the exchange you see before the step 9 (including the certificate exchange) is vulnerable because only after it the channel is secured.
P.S. You may be interested in reading this.
Yes, the client certificate is sent in the clear if the server sent a certificate request.
Some servers (IIRC, Microsoft IIS) first perform handshake with no user authentication and then start a renegotiation asking for client certificate. The renegotiation is thus encrypted using the cipher suite negotiated in step 1 and the client certificate is encrypted on the wire.
If in doubt, use wireshark.