Kalido Understood on your configuration setup. I would recommend moving away from sending traffic to a specific node because this messes with any persistence that you might want to configure. You really should have a pool configured for each path that you are going to balance traffic for and use the forward to pool option instead. Using pools will ensure that persistence functions as expected, allows you to add additional members for a specific URI path or Host field without much of a change to the virtual server, and finally this allows you to run health monitors at a level that doesn't effect the entire node if by chance this node is working for one URI path or Host field but not others.
In regards to client and server SSL profile, this configuration can be found under the VS with labels SSL Profile (Client) and the other as SSL Profile (Server). For the HTTP profile you can also see that under the virtual server and the configuration box says HTTP Profile next to it. Based on your previous statment you would have to have 1 or both SSL profiles and an HTTP profile configured already for it to be working for other URI paths so probably something you don't have to worry about but you can verify what is configured.
Now in regards to 8443 if you run the following tcpdump you should be able to see if the F5 is issuing the reset or if it's the server. Most likely based on your description it is the server issuing the reset which typically means the server is either blocking because of a local OS firewall rule, the server isn't listening on 8443, or the server isn't expecting HTTPS traffic on port 8443. By "<f5_selfIP_closest to serverIP>" this would be the interface the traffic leaves the F5 on when attempting to reach the destination node. Replace the entirety of the pieces below from < to > for the appropriate IP.
tcpdump -nni 0.0:nnp host <f5_selfIP_closest to serverIP> and host <nodeIP> and port 8443
The following is an example of what the command would look like if the selfIP of the F5 was 10.10.10.1 and the destination node IP is 10.10.20.30.
tcpdump -nni 0.0:nnp host 10.10.10.1 and host 10.10.20.30 and port 8443
Hopefully this all makes sense and helps you resolve the issue at hand.