A virtual server which caters to both HTTPS and plain TCP traffic on the same port.

you could try something like in this link:

https://devcentral.f5.com/articles/handling-http-requests-on-an-https-virtual-server-31668

Now HTTPs using the default pool and setting something like this for http :

when CLIENT_ACCEPTED { set https_state 0 }

when CLIENTSSL_HANDSHAKE { set https_state 1 }

when HTTP_REQUEST { if { [$https_state eq 0] } { pool xxxx } }