You can use an AWS VPC VPN connection to access your ElastiCache Instance.
The detailed steps are described in the AWS Documentation Accessing Elasticache Resources from Outside AWS.
Basically you have to do the following steps:
- Create a ElastiCache as you would do normally
- Create a NAT instance and configure it to forward traffic to your ElastiCache Instance
It might be easier for you to create a AWS EC2 instance and use it to access your ElastiCache and run your debugging commands from there. You might can also use, for example SSH port forwarding to tunnel your traffic through the additional instance.
Pleason Note:
From the Amazon ElastiCache Documentation:
Accessing Amazon ElastiCache
Your Amazon ElastiCache instances can only be accessed through an Amazon EC2 instance.
If you launched your ElastiCache instance in an Amazon Virtual Private Cloud (Amazon VPC), you can access your ElastiCache instance from an Amazon EC2 instance in the same Amazon VPC or, by using VPC peering, from an Amazon EC2 in a different Amazon VPC.
ElastiCache is designed for the usage from EC2 only. Therefore I would recommend you to only use the above solution for testing and debugging.