Does backend pool member host multiple domains?
I am wondering if it uses SNI to determine the page being requested, but when you perform SSL bridging on the F5 no SNI is presented to the webserver. It may then default to a domain for which 'GET /' doesn't have any associated content.
What was the tcpdump command used to produce the output you provided above?
You could do a tcpdump on the F5 VS, i.e. F5 clientside, to capture the TLS establishment - the server name extension in the client hello would show what is being requested. As a quick check you could copy this into the Server Name field within the server SSL profile. Note that if that turned out to be the issue you would need a longer term solution to insert the appropriate SNI on the serverside. Devcentral has a few iRule options, but I think later versions of software may now allow it to be done automatically.