Can the F5 Bigip act as a proxy for a specific VIP

I don't think mine is an "answer" so I put it as "comment" There are 2 types of traffic you mentioned, one from your web server (those pool member), the other from "external servers" these links from your web server/pages. If you want to, you can re-write these external link from "HTTP" to "HTTPS", but are those external web server going to support HTTPS if you change it?? Please make sure that server support HTTPS and then you can change them.. actually be better modify the web page links (at your web server) from http to https... F5 LTM is load balance device, traffic balance by it but not provide by it.