your options for SSL traffic are:
passthru, no client side or server side on the vip (you cant use cookie or do any kind of irules / inspection with this)
Offloading Client side on vip - no server side, this will decrypt traffic and send clear case back to server.
Bridging - both client side and server side SSL certs are needed. ** unless you are changing something in the profile to add value, you should use serverssl. Adding the client side cert to the server side of the f5 - makes things mess when it comes to updating certs and or reading tcpdumps etc.
https://community.f5.com/t5/technical-forum/ssl-passthrough-ssl-offloading-and-ssl-bridging/td-p/197081
You have not addressed:
is this internal only - or on the internet ?
Is there something you are trouble shooting and you are sure you are accuratly looking at the correct conversation or are you trying to clean the noise in the logs.