Depending on your expected traffic patterns and volume, no responses to report for an extended period of time is its own data point.
No 2XX-499 results means the server is borked.
If you wanted to be really fancy you could send heartbeat requests when no live traffic had hit that node for n milliseconds.
I still think the latter is the right answer. Why inflate traffic when you are horizontally scaling? That’s a lot of health checks per second.