'EC2 Instance not available in ECS

I have created an EC2 instance via Terraform with the following configuration:

EC2 instance is using the latest Amazon ECS-Optimized Amazon Linux 2 AMI.
Instance is sitting in a private subnet, with a route to a NAT GW. Tested internet connectivity fine.
SG rules are configured correctly.
EC2 Instance profile is using AmazonEC2ContainerServiceforEC2Role
EC2 user-data is configured (with my cluster name) with:

echo ECS_CLUSTER=my-cluster-name >> /etc/ecs/ecs.config

When I go to my ecs-cluster, no instances show in the EC2 Instance section of the console.

Is there anything else I'm missing as to why this cluster can't register with the EC2 instance?

amazon-ecs

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