I'm trying to do something very similar to this.
When I configured my ECS service to run my container inside public subnets and auto-assign it a public IP address, everything worked fine and it passed the health check. But for some reason, if I try using my two private subnets (and disabling the auto-assign IP address option), it stops working.
I've already checked my security groups. It's a single one for both the ALB and the ECS service, which allows traffic from everywhere on ports 80, 8080 (the one my container is listening to) and from any port coming from the same security group (so that the ALB can use other ports during the health check). The health check path is also working fine.
What am I doing wrong?