[EKS] [issue]: Unable to resolve EKS cluster private endpoint from worker node

**Tell us about your request**
Created an EKS cluster in existing VPC using eksctl and changed endpoint to private. After I did this, I am unable to access the private endpoint even from the worker host.

**Which service(s) is this request for?**
EKS

**Tell us about the problem you're trying to solve. What are you trying to do, and why is it hard?**
The cluster was created using eksctl:
`eksctl create cluster \
--name _my-eks-aws_ \
--version 1.13 \
--nodegroup-name standard-workers \
--node-type t2.medium \
--nodes 2 \
--nodes-min 1 \
--nodes-max 3 \
--node-ami-family Ubuntu1804 \
--vpc-private-subnets _my-subnet-1,my-subnet-2_ \
--verbose 4 \
--node-private-networking \
--ssh-access --ssh-public-key=~/.ssh/_my_key.pub_`

this gave me a cluster with public access enabled (kubectl from my host worked), so I disabled that and enabled private endpoint.

Tried using a linux bastion host (https://aws.amazon.com/quickstart/architecture/linux-bastion/) but thought maybe I should try it from the worker node first. Neither worked
`root@ip-my-ip:~# dig _xyz_.us-west-2.eks.amazonaws.com

; <<>> DiG 9.11.3-1ubuntu1.9-Ubuntu <<>> _xyz_.us-west-2.eks.amazonaws.com
;; global options: +cmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NXDOMAIN, id: 31082
;; flags: qr rd ra; QUERY: 1, ANSWER: 0, AUTHORITY: 1, ADDITIONAL: 1

;; OPT PSEUDOSECTION:
; EDNS: version: 0, flags:; udp: 4096
; COOKIE: xyx (good)
;; QUESTION SECTION:
; _xyz_.us-west-2.eks.amazonaws.com. IN A

;; AUTHORITY SECTION:
xyz.eks.amazonaws.com. 5 IN SOA xyz. 1 7200 900 1209600 86400

;; Query time: 23 msec
;; SERVER: 10.43.1.12#53(10.43.1.12)
;; WHEN: Thu Oct 03 15:09:09 UTC 2019
;; MSG SIZE rcvd: 198`

**Are you currently working around this issue?**
Using private cloud

**Additional context**
Was trying to setup private cluster endpoint using instructions mentioned here:
https://github.com/aws/containers-roadmap/issues/221
https://aws.amazon.com/blogs/compute/enabling-dns-resolution-for-amazon-eks-cluster-endpoints/
https://docs.aws.amazon.com/en_pv/eks/latest/userguide/cluster-endpoint.html#private-access

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Any help will be greatly appreciated.

Start with the EKS private endpoint documentation and the linked AWS blog and roadmap issue, then compare their DNS requirements with the worker-node `dig` output in this report. Done means the private EKS endpoint resolves from the worker node or bastion host and can be accessed as intended.

Written by the indexing model from the issue text.