The git-parameter-plugin shows a simple select list from which to find a branch/git.

If the list of branches/tags is very long, finding the right branch is hard.

Scrolling to the right entry becomes near impossible when more items are skipped in a single pixel scroll than can be shown in one "page" of the list.

Perhaps update the UI component with some sort of search/filter or autocomplete feature where you can type in part of the branch/tag you want and have the list filter down to branches/tags matching that text.