How to mark Pod as ready if one of the containers has completed

Question

I have a Pod that has two regular (i.e. not Init) Containers. One of them is meant to be used as a "job", i.e. it should run a script and then exit while the other container should keep running. The problem is that as soon as the "job" container is finished, the Pod will be marked as NotReady due to all containers not being Ready. Can I somehow make this "job" container for Pod-readiness optional? Is there anything better than having sleep 1000000000 in the "job" container's command?

Note that:

• I cannot make this "job" container an InitContainer because it cannot run before the other container
• I could use a k8s Job for that although it'd be way easier for my specific use-case to run this "job" container in the same Pod as I'd like it to share network and some volumes with the other container. Jobs unfortunately cannot "bind" to an existing Pod.