Nginx - Reverse proxy serving ScreenConnect does not prepend subdirectory

Question

I am running an unsecured ScreenConnect web interface on a machine on my local network. I would like to serve it through port 443 using nginx's reverse proxy, and access it via:
https://<WAN.IP.ADDRESS>/screenconnect

My nginx.conf location block:

            location / {
            root /www/var/nginx/html
            }

            location /screenconnect/ {
            proxy_pass                              http://local.screenconnect.server:8040/;
            proxy_buffering                         off;
            proxy_set_header Host                   $host;
            proxy_set_header X-Real-IP              $remote_addr;
            proxy_set_header X-Forwarded-For        $proxy_add_x_forwarded_for;
            proxy_set_header X-Forwarded-Proto      $scheme;
            }

I am successful in getting to the Screen Connect Web Interface, and the url reads as
https://<WAN.IP.ADDRESS>/screenconnect/

However, any additional subdirectories that I access, such as https://<WAN.IP.ADDRESS>/screenconnect/login.php? will drop the /screenconnect/ subdirectory and try to access https://<WAN.IP.ADDRESS>/login.php?
This throws me a 404 error.

Things I've tried

• I've inserted /screenconnect/ to https://<WAN.IP.ADDRESS>/login.php?/ and got https://<WAN.IP.ADDRESS>/screenconnect/login.php?, which gives me the site I need.
• I've adjusted the web.config file on my screenconnect server and appended the correct directory:
  <add key="WebServerAddressableUri" value="https://WAN.IP.ADDRESS:443/screenconnect/" />
• I've tried removing the / at the end of proxy_pass http://local.screenconnect.server:8040/; and location /screenconnect/
• I've also tried a host of different simple directives for the location block from people who have had related problems
  
• I've replaced the IP of the screenconnect server with an apache server running on port 80 that has a simple html page, which redirects to a subfolder. When redirecting, the /screenconnect/ directory is prepended correctly.