It's a program with no blocking I/O, so if the eyes stop moving, you know you're looking at a certain kind of connectivity issue. If some more complicated app stops responding, the problem space of where to start troubleshooting is much larger.
If you miiiiight have a flaky network, leaving xeyes open in the corner can be a real headache-saver.
If you miiiiight have a flaky network, leaving xeyes open in the corner can be a real headache-saver.