Quick and dirty: Use [] to initialize an arrayref. Also, arrow notation makes most things clearer to me.

sub checkForm {
  my (..., $items2show_ref) = @_;
  $items2show_ref = [];
  $items2show_ref->[ARRAYX] = [];
  # ...
  push @{ $items2show_ref->[ARRAYX] }, $value;
}
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Good luck cleaning up the old code, by the way. That sort of pastime caused a good 50% of my gray and missing hairs.