You can get ReminderMinutesBeforeStart Directly from the $message object.
Here is a modified segment (tested) of your code:

---<snip>---
my $CalendarFolderItems = $folder->Items;
print length($folder) . "\n";

for my $itemIndex (1..$CalendarFolderItems->Count)
{
  my $CalendarItem = $CalendarFolderItems->item($itemIndex);
  next if not defined $CalendarItem;

   $start_date     = $CalendarItem->{Start}->Date;
   $start_time     = $CalendarItem->{Start}->Time;
   $end_date    = $CalendarItem->{End}->Time;
   $end_time    = $CalendarItem->{End}->Time;
   $duration    = $CalendarItem->{Duration};
   $subject     = $CalendarItem->{Subject};
   $categories     = $CalendarItem->{Categories};
   $body    = $CalendarItem->{Body};
   $reminder    = $CalendarItem->{ReminderMinutesBeforeStart};
   # AppointmentItem.ReminderSet
    print "*****************************************\n";
---<snip>---
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