Syslog TCP SSL input with NGINX reverse proxy

Did you try TCPDUMP on graylog server see if you can see the remote client?

tcpdump_info

Your are send syslog TCP with Nginx proxy using certificates for port 10516 with listen 10.10.10.1:10516 ssl. this would be TCP/TLS.
If this is correct then the INPUT should reflect with those certs I do believe. Troubleshooting would be is to disable your SSL and tried it with just

listen 10.10.10.1:10516;

Also one of our cummunity members posted this,