It would be good to have an option or setting the most top of results to be chosen by default.
Do you check it on version 0.6.1 whether built a plugin from source (branch https://github.com/jenkinsci/git-parameter-plugin/tree/feature/JENKINS-31939)?
I have added my screenshots with plugin version and with 2 types of job run:
1) by timer
It does not work from you because these changes have not yet been merged.
I made only pull request, so you can see whether such a change is right for you. At version 0.6.1 will not work, as you want.
If you want to use it you must wait to release 0.6.2 or compile plugin from source.
will wait for 0.6.2