Health indicator for Eureka client reports UP when not connected to server

Describe the bug
If Eureka server is not available, Health indicator for Eureka client will always report that it is UP. One such sample from Spring Cloud Gateway:

{
  "status": "DOWN",
  "components": {
    "discoveryComposite": {
      "status": "UP",
      "components": {
        "discoveryClient": {
          "status": "UP",
          "details": {
            "services": []
          }
        },
        "eureka": {
          "description": "Eureka discovery client has not yet successfully connected to a Eureka server",
          "status": "UP",
          "details": {
            "applications": {

            }
          }
        }
      }
    },
    "reactiveDiscoveryClients": {
      "status": "UP",
      "components": {
        "Simple Reactive Discovery Client": {
          "status": "UP",
          "details": {
            "services": []
          }
        },
        "Spring Cloud Eureka Reactive Discovery Client": {
          "status": "UP",
          "details": {
            "services": []
          }
        }
      }
    },
    "redis": {
      "status": "DOWN",
      "details": {
        "error": "org.springframework.data.redis.RedisConnectionFailureException: Unable to connect to Redis"
      }
    },
  }
}

These are the lines which specifically say that Health indicator should report UP: https://github.com/spring-cloud/spring-cloud-netflix/blob/b6353637c97e3044967ae44bda5c3377b63a4ee1/spring-cloud-netflix-eureka-client/src/main/java/org/springframework/cloud/netflix/eureka/EurekaHealthIndicator.java#L76-L77 and https://github.com/spring-cloud/spring-cloud-netflix/blob/b6353637c97e3044967ae44bda5c3377b63a4ee1/spring-cloud-netflix-eureka-client/src/main/java/org/springframework/cloud/netflix/eureka/EurekaHealthIndicator.java#L80-L81

Not sure why it was done this way, but I don't think this is right. If Eureka client cannot connect to Eureka server the application should report as DOWN at least for readiness probe.

Sample
Just take standard Spring Cloud Gateway application, add Spring Cloud Netflix Client dependency to it, and start the gateway. For visibility add:

management.endpoints.web.exposure.include=health
management.endpoint.health.show-details=always

Start with spring-cloud-netflix-eureka-client/src/main/java/org/springframework/cloud/netflix/eureka/EurekaHealthIndicator.java, especially the lines linked in the issue. Reproduce the behavior with a standard Spring Cloud Gateway application and the listed health settings while Eureka is unavailable. Done means the Eureka health indicator reports DOWN when it has not connected to a Eureka server.