There is not documentation on how to connect Data Connect service to a Cloud SQL instance with Private IP. Deployment simply fails with timeout error.
Had to open a support case to learn that I have to run the deployment command from within the same VPC. This should be at least documented. The deployment script could be improved, so that you don't have to run the deployment from a VM. The steps that are failing should be executed from the service directly, we'd just need to grant the required permissions to the SA.