TIMTOWTDI

Alternate approach; closer to OP's original (and a surprise to me that it appears to work!)

#!/usr/bin/perl
use 5.016;
use warnings;
use strict;

my $prev_ctrlc = 0;

if( ($prev_ctrlc == 0) || ($prev_ctrlc == 1) ) {
   $SIG{'INT'} = \&control_c_observed;
   sleep 1;
   for (1..1e3) {
        say "\t nothing yet";
        sleep 2;
   }
}


sub control_c_observed {
   if ($prev_ctrlc == 0) {
     print "Second ctrl-c within 2 seconds required\n";
     $prev_ctrlc = 1;
    } else {
        $prev_ctrlc++;
    }
   if ($prev_ctrlc == 2 ) {
     say "OK, that's two of 'em!";
     exit;
   } 
}
[download]

Sample run:

C:\>C:\SQLite\1018190.pl
         nothing yet
         nothing yet
         nothing yet                 # single tap here
Second ctrl-c within 2 seconds required
         nothing yet
         nothing yet                 # double tap here
OK, that's two of 'em!

C:\>
[download]

The sleep's could annoy your users, as they might seem like the machine is (briefly) locking up.