I would like to be able to push tags on SUCCESS or UNSTABLE, but not on FAILURE. Currently this is not possible. I see that the pull request was denied...any chance of getting functionality like this into the plugin?

Adam Kaufman that functionality won't be added into the plugin unless someone reworks the submission based on the feedback that was provided on the submission. Since the pull request was closed about 2 years ago, it is unlikely that will arrive in the plugin.

Once again Jenkins kicks you in the teeth for using the fancy features. Just go with a shell script

git push origin $GIT_LOCAL_BRANCH 

in last build step wrapped with a conditional. https://wiki.jenkins-ci.org/display/JENKINS/Conditional+BuildStep+Plugin
You need the credentials available via CLI for that – we use Docker, so we just put ssh keys in Dockerfile but you could also use one of the plugins for managing secrets.

Above works, unless you have other publishers that can change the status (like me).
You could try https://wiki.jenkins-ci.org/display/JENKINS/PostBuildScript+Plugin but it's unmaintaned and I haven't yet checked if it isn't afflicted by a similar bug as this.
The https://wiki.jenkins-ci.org/display/JENKINS/Post+build+task only let's you grep console, which is too ugly for my taste.

Last resort is a groovy/shell script checking the build status manually and calling git push based on that.

Mark Waite would it be possible to at least update the documentation which is clearly wrong? Currently the publisher will only push on "Stable" status not "Successful".
I know about JENKINS-10763 , but what the permalinks show (lastSuccessfullBuild vs lastStableBuild) is quite prominent so I'd go with that.

Jakub Bochenski, the wiki page for documentation is available for anyone to edit and improve. Please feel free to improve it.

The online help is available in the source code repository for anyone to clone and submit pull requests. Please feel free to submit a pull request to improve it.