Log output comes from stdout/stderr of the running container. If you do not see any output it would imply that localstack/localstack:latest is not generating any output to stdout/sterr, in which case you would need to work with the owners of that image to understand why that is the case.
However, looking at your pipeline it is possible that the pipeline starts and then quickly stops. Perhaps you are not giving your service container enough time to initialize and start up, which is why no logs are displayed?
Either way, Drone streams service container output by default, no special configuration required.
It looks like you are using the experimental Kubernetes runtime which is not recommended for production use due to its experimental status and known issues . You should instead consider using agents. You can certainly use the experimental Kubernetes runtime, but you should expect to get hands on with the code. We provide a guide for debugging the experimental runtime and sending patches