Rsyslog can't start inside of a docker container

Question

I've got a docker container running a service, and I need that service to send logs to rsyslog. It's an ubuntu image running a set of services in the container. However, the rsyslog service cannot start inside this container. I cannot determine why.

Running service rsyslog start (this image uses upstart, not systemd) returns only the output start: Job failed to start. There is no further information provided, even when I use --verbose.

Furthermore, there are no error logs from this failed startup process. Because rsyslog is the service that can't start, it's obviously not running, so nothing is getting logged. I'm not finding anything relevant in Upstart's logs either: /var/log/upstart/ only contains the logs of a few things that successfully started, as well as dmesg.log which simply contains dmesg: klogctl failed: Operation not permitted. which from what I can tell is because of a docker limitation that cannot really be fixed. And it's unknown if this is even related to the issue.

Here's the interesting bit: I have the exact same container running on a different host, and it's not suffering from this issue. Rsyslog is able to start and run in the container just fine on that host. So obviously the cause is some difference between the hosts. But I don't know where to begin with that: There are LOTS of differences between the hosts (the working one is my local windows system, the failing one is a virtual machine running in a cloud environment), so I wouldn't know where to even begin about which differences could cause this issue and which ones couldn't.

I've exhausted everything that I know to check. My only option left is to come to stackoverflow and ask for any ideas.

Two questions here, really:

1. Is there any way to get more information out of the failure to start? start itself is a binary file, not a script, so I can't open it up and edit it. I'm reliant solely on the output of that command, and it's not logging anything anywhere useful.

2. What could possibly be different between these two hosts that could cause this issue? Are there any smoking guns or obvious candidates to check?

Regarding the container itself, unfortunately it's a container provided by a third party that I'm simply modifying. I can't really change anything fundamental about the container, such as the fact that it's entrypoint is /sbin/init (which is a very bad practice for docker containers, and is the root cause of all of my troubles). This is also causing some issues with the docker logging driver, which is why I'm stuck using syslog as the logging solution instead.