Following the Official Guide I got to the section onForwarding to ExtternalNames. Where it says:

When specifying an ExternalName, Træfik will forward requests to the given host accordingly

which points to the docs from kubernetes services without selectors

Which led me to create a service

kind: Service
apiVersion: v1
metadata:
  name: my-service
  namespace: prod
spec:
  type: ExternalName
  externalName: my.database.example.com

Of which Traefik happily ignores when I point to it:

---
apiVersion: extensions/v1beta1
kind: Ingress
metadata:
  name: my-service
  namespace: kube-system
spec:
  rules:
  - host: my-service.example.com
    http:
      paths:
      - path: /
        backend:
          serviceName: my-service
          servicePort: 4080

I have also tried as an endpoint.

---                                                                                                                                                                                           
kind: Service
apiVersion: v1
metadata:
  name: my-service
  namespace: kube-system
spec:
  ports:
  - protocol: TCP
    port: 80
    targetPort: 4080
---
kind: Endpoints
apiVersion: v1
metadata:
  name: my-service
subsets:
  - addresses:
      - ip: 10.0.0.3
    ports:
      - port: 4080

Does anyone know how to get traefik to point to an externalname as the documentation suggests?