If you want to configure a job just to build tags, do the following:
Configure Bitbucket Server
Advanced Configuration > Branch Options > Build All is selected. 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
+refs/tags/*:refs/remotes/origin/tags/*. Set the branch specifier to
**/tags/**. This will configure the job so it only responds to new tags.