Lighttpd Reverse Proxy with SSL/HTTPS

I am trying configure Lighttpd to redirect/handle port-specific requests to a subdomain.

I can access my plex server via https://www.example.com:32400/

I would like that to be redirected to https://plex.example.com/

I have the following config, but there isn't any SSL associated with the link. SSL is working fine on the main page, but nothing else.

$HTTP["host"] == "plex.example.com" {
    proxy.server  = ( "" => ( (
            "host" => "127.0.0.1",
            "port" => 32400
    ) ) )
}

See: https://redmine.lighttpd.net/projects/lighttpd/wiki/Docs_ModProxy

lighttpd mod_proxy is a reverse proxy. lighttpd mod_proxy does not currently support SSL/TLS connections to the backend server.

If you want to use lighttpd as your reverse proxy, you would need to disable HTTPS on the backend (Plex) service.

Other tools would work, like a port forward using iptables. (This assumes tht the application does not use absolute links to itself, for which a more complicated solution, like Apache's mod_proxy_html to rewrite modifiy the returned data to fix the links)