you can use a traefik backend health check defined in your k8s ingress through annotations. This way you don't forward to backends that are not active. For example:
kind: Ingress
metadata:
  name: specific-deployment
  annotations:
    traefik.backend.healthcheck.port: 8080
    traefik.backend.healthcheck.scheme: http
    traefik.backend.healthcheck.path: /health   
spec:
  rules:
  - host: specific.minikube
    http:
      paths:
      - path: /
        backend:
          serviceName: stilton
          servicePort: http
This way you can use the k8s readiness probes for your pods.