One way you can reduce typing and speed up assignment is to concentrate on the hash you are assigning to:

while( @result_array = $query->fetchrow_array ) {
   my $col = $self->{fields}{$result_array[2]};
   $col->{Object_ID}  = $result_array[0];
   # and so on ...
}
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You could create an array that maps array numbers to column names:

my @name =  qw|Object_ID ID ...|;
while( @result_array = $query->fetchrow_array ) {
   my $col = $self->{fields}{$result_array[2]};
   for my $pos(@name) {
      $col->{$name($pos)}  = $result_array[$pos];
   }
   $self->{fields}{$result_array[2]}{Value}  = "";
    $self->{display_order}{$result_array[16]} = $result_array[2];
}
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