CertChk + Redirect

Something like this could do the trick. You may have to tweak to your needs. You will also need to set your client auth in your client SSL profile to request.

https://devcentral.f5.com/wiki/iRules.X509__subject.ashx

https://devcentral.f5.com/wiki/iRules.SSL__cert.ashx

when HTTP_REQUEST {
    if {[SSL::cert count] > 0}{
        set cert_subject [X509::subject [SSL::cert 0]]
        if {$cert_subject equals "CN..."}{
            return
        }
        else {
            if cert doesn't contain required subject, redirect
            HTTP::respond 302 noserver Location "https://someurl"
        }
    }
    else {
        if no cert presented, redirect
        HTTP::respond 302 noserver Location "https://someurl"
    }
}