TLS 1.2 breaks SQL Server linked servers
Are you familiar with using any tools such as netmon, wireshark, or netsh?  You might want to do a capture as you replicate this issue.  Something that sticks out in my mind is Server B might be trying to hit something external to the mix (i.e. Certificate Revocation List CRL check) and that call is failing.  A CRL check takes place on the client side of the equation - in this case Server B is the client.  If you are able to run a trace you probably want to filter for tcp resets where the client (Server B) is involved.  In wireshark a filter for this would look like tcp.flags.reset == 1 and ip.addr == 10.X.X.X where 10.X.X.X would be the ip address of Server B.