How to get the output of container_commands after deployment?

Not a console view, but it is (now) visible in the logs.

.ebextensions/10-log.config

container_commands:
  05-whoami:
    command: "whoami"

/var/log/cfn-init.log after deployment

2014-07-01 22:08:10,695 [DEBUG] Running command 05-whoami
2014-07-01 22:08:10,695 [DEBUG] Generating defaults for command 05-whoami
2014-07-01 22:08:11,014 [DEBUG] Defaults script for 05-whoami output: {"env":{"EB_REQUEST_ID":"110d0932-016c-11e4-9f71-3fe967c5cd60", [long list of params omitted for brevity]}
2014-07-01 22:08:11,015 [DEBUG] No test for command 05-whoami
2014-07-01 22:08:11,050 [INFO] Command 05-whoami succeeded
2014-07-01 22:08:11,050 [DEBUG] Command 05-whoami output: root

Reply from the AWS support:

The easiest way to see the output would be to pipe the command or script output to a file using >>. Unfortunately there isn't a live console that can be viewed to show the process live.

So unfortunately there is no way to do that (yet).