"health checks" are better broken down into "liveness" and "readiness" checks. You often want separate timings for the initial startup phase as well.

If your platform only has one "health check", figure out first if it'll be handled like a liveness check (restarting/recreating the instance) or readiness check (merely taking it out of load-balancer backends), before you follow any kind of generic best-practice that might be using the same term in a different way.