This following trick will show you how to always display the Search textbox on Select2 control.
Enable Requires search option under Fields setup -> Edit Tag pane -> choose Select -> SELECT Tag.
Put this following code in Server Events -> Global -> All Pages -> Page_Head:
<script> ew.selectMinimumInputLength = 0; // Minimum number of characters required to start a search ew.selectOptions.minimumResultsForSearch = 0; // Minimum number of results required to display the search box </script>
Re-generate ALL the script files again, and enjoy the result.