After some more tinkering with the Raspberry Pi Dramble (a cluster of 6 Raspberry Pis used to demonstrate Drupal 8 deployments using Ansible), I finally was able to get the RGB LEDs to react to Nginx accesses—meaning every time a request is received by Nginx, the LED toggles to red momentarily.
This visualization allows me to see exactly how Nginx is distributing requests among the servers in different load balancer configurations. The default (not only for Nginx, but also for Varnish, HAProxy, and other balancers) is to use round-robin distribution, meaning each request is sent to the next server. This is demonstrated first, in the video below, followed by a demonstration of Nginx's
ip_hash method, which pins one person's IP address to one backend server, based on a hash of the person's IP address: