Active-Passive Jenkins Setup in Kubernetes

This contradicts with how one should IMHO run applications in Kubernetes. Active/passive is a concept for the past century.

Instead, configure a health check for the Jenkins Deployment. If that fails, Kubernetes will automatically kill the task and start a replacement (which will be available only a few seconds after detecting the active one being unhealthy).

There have been active considerations to emulate active/passive setup for containers, but note that as a product feature this really is not a must have and hence not built in. This very well may be implemented as an OOB feature integration wherein you have to craft your applications to at least do the following:

1. General leader election (for master selection and traffic routing,maybe a sidecar container to do elections and message routing)
2. Make the liveness/readiness probe detection routines (and the failover logic) to patch all pods under failed paradigm to no longer be selected via any pod selector equation
3. In the event of another failover, you will still have to ensure another patch of labels (and this time across the old and new pods) to update pods metadata aka labels

If you are looking for something bare minimal than, configuring liveness/readiness probes may just do the trick for you. As always, you should avoid getting into a practice of mass mutating pod labels with ad-hoc patches for role selection

https://github.com/kubernetes/kubernetes/issues/45300

If you are OK with an opinionated framework , then JenkinsX may help you. It comes by default with the features as required by you.