该问题的解决方法是通过检查EC2实例的安全组规则和网络ACL规则，以确保正确的网络流量可以到达EKS实例。此外，还可以检查VPC的路由表设置，以确保流量被正确路由到EKS集群。以下是一个示例Python脚本，它使用boto3库检查EC2实例的网络设置：

import boto3

# replace with the appropriate AWS region
region_name = 'us-west-2'

# replace with the ID of the EC2 instance
instance_id = 'i-0123456789abcdef0'

# create a client object for EC2
ec2 = boto3.client('ec2', region_name=region_name)

# describe the security groups associated with the instance
response = ec2.describe_instances(InstanceIds=[instance_id])

# retrieve the security group IDs associated with the instance
security_group_ids = response['Reservations'][0]['Instances'][0]['SecurityGroups']
security_group_ids = [sg['GroupId'] for sg in security_group_ids]

# describe the security groups and their rules
response = ec2.describe_security_groups(GroupIds=security_group_ids)

# display the security group rules
for sg in response['SecurityGroups']:
    print(f'Security Group: {sg["GroupId"]}')
    for rule in sg['IpPermissions']:
        print(f'- Protocol: {rule["IpProtocol"]}, '
              f'Ports: {rule["FromPort"]}-{rule["ToPort"]}, '
              f'Sources: {rule["IpRanges"]}')

该代码将打印与EC2实例相关联的每个安全组的IP规则。可以使用类似的方法检查网络ACL规则和VPC路由表设置，以帮助解决AWS EKS EC2实例可达性检查失败的问题。