If you want to configure a job just to build tags, do the following:

Configure Bitbucket Server

Make sure  Advanced Configuration > Branch Options > Build All is selected in the hook configuration. This will skip the whitelist and blacklist checks so that all new commits and tags send the required Jenkins notification.

Set up a Jenkins Job for Tags

In the job set refspec to +refs/tags/*:refs/remotes/origin/tags/*. Set the branch specifier to refs/tags/**. This will configure the job so it only responds to new tags.