I have succesfully set up an IPsec tunnel between the F5 and remote device. I have HTTPS server configured on the remote end and on a client I able to connect to the HTTPS server when using the F5 internal interface as the default gateway on the client.
I have succesfully set up the explicit forward proxy and when I configure the client to point to the virtual server I am able to proxy web traffic out to the Internet. (Bypassing the IPsec tunnel and going to the Internet)
However I am not able to force the proxied traffic over the IPSEC tunnel succesfully to reach my HTTPS server on the remote end.
The https server is not the one that you have configured with IPSEC tunnel to the f5 device, right it another device?
I have not tried your settup before but if you send traffic to the F5 device to a normal virtual server maybe with a pool member the web server or a forwarding VS that will use the routing table that should point to the route do you see the traffic using the ipsec tunnel? Basically to confirm that not only the tunnel is up but the routing rules for inserting traffic in the tunnel work (having static route for the destination going to the tunnel or traffic selectors https://techdocs.f5.com/kb/en-us/products/big-ip_ltm/manuals/product/bigip-tmos-tunnels-ipsec-13-0-0... )? The wildcard SSL and wildcard forwarding IP virtual servers that are connected by http tunnel the to explicit VS I think will select the ipsec tunnel to destination web server if your routing is correct.
If nothing works also have you tried proxy chaining to send the traffic to the IPSEC device ?