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I will try to answer this one,
The server ssl profile is for acting as an ssl client. Since, we are talking about Client Authentication here, if the certificate on your node has a server, I'd assume that you need re-enryption to your server too.
In addition, in client authentication, the server challenges the client for authentication. The client,in this case the BIGIP authenticates [using its private key] itself by sending a digital signature back to server ( node ). Because, the server now has the clients public key, pre master secrets come into play on the server side of the connection.
If the certificates on your server-ssl profile and the server are the same, i would assume there should be an SSL handshake failure.