How does one forward a client authentication certificate through HA proxy while terminating TLS?

You can set various HTTP headers to be sent to the backend regarding the TLS client certificate that was presented. For example:

frontend intranet
    bind 10.20.30.40:443 ssl crt /etc/haproxy/pem/server.pem ca-file /etc/haproxy/pem/client-chain.pem verify required
    http-request set-header X-SSL                       %[ssl_fc]
    http-request set-header X-SSL-Client-Verify         %[ssl_c_verify]
    http-request set-header X-SSL-Client-SHA1           %{+Q}[ssl_c_sha1]
    http-request set-header X-SSL-Client-DN             %{+Q}[ssl_c_s_dn]
    http-request set-header X-SSL-Client-CN             %{+Q}[ssl_c_s_dn(cn)]
    http-request set-header X-SSL-Issuer                %{+Q}[ssl_c_i_dn]
    http-request set-header X-SSL-Client-Not-Before     %{+Q}[ssl_c_notbefore]
    http-request set-header X-SSL-Client-Not-After      %{+Q}[ssl_c_notafter]
    default_backend your_backend

Your application must then examine the headers and take appropriate action.

This example was taken from raymii.org where you may find some additional useful information about using client certificates with HAProxy, such as validating the client certificate and rejecting invalid certificates.