Expose the stopped reason from AWS Console UI in the runner itself

During the recent Gitlab Registry downtime (see gitlab-com/gl-infra/production#2381 (closed)) Task Definition was not able to pull the container from the registry. Can we somehow expose the actual ECS error ("stopped reason" - see screenshot) in the runner itself?

This is what I'm seeing in the runner:

 ERRO[2020-07-08T17:32:53Z] Application execution failed                  
PID=26075 error="waiting Fargate task to be ready: waiting for Fargate task to be in running state: 
error waiting AWS Fargate Task \"arn:aws:ecs:us-west-2:[redacted]:task/FargateRunnerStack-FargateGitlabRunnerCluster4AA9D65B-PIFETFdZdJpv/d729507e9c0946579ff8ed2eb86a603c\" 
to be in \"Running\" state: ResourceNotReady: failed waiting for successful resource state"

..but the real reason is spelled out here: