[In reply to updated question, where the OP attempts to use fork.]

Close. You'll never reach to waitpid. Also, system(...); exit(); is the same as exec(...);

I believe the code below is a robust (allows for missed polls or missed twitches), reusable (a user-provided function indicates when to stop polling) and fancy (seperate timers for polling and twitching) solution. (Untested)

use POSIX       qw( WNOHANG    );
use Time::HiRes qw( time sleep );

sub min { $_[0] < $_[1] ? $_[0] : $_[1] }
sub max { $_[0] > $_[1] ? $_[0] : $_[1] }

sub twirling_baton {
   my ($twitch_interval, $poll_interval, $poll_func) = @_;

   my $af = ($| = 1);

   my $tcount = 0;
   my @baton  = qw( | / - \ );
   print($baton[0]);

   my $time = time;
   my $twitch_time = $time + $twitch_interval;
   my $poll_time   = $time + $poll_interval;

   for (;;) {
      sleep(max(min($twitch_time, $poll_time) - $time, 0.250));

      # Sleep is not precise.
      $time = time;

      if ($time >= $poll_time) {
         last if &$poll_func();
         $time = time;  # In case the call is slow.
         $poll_time = $time + $poll_interval;
      }

      if ($time >= $twict_time) {
         $tcount = ($tcount + 1) % @baton;
         print("\b", $baton[$tcount]);
         $twitch_time = $time + $twitch_interval;
      }
   }

   $| = $af;
}

$pid = fork;

if (not defined $pid) {
   die("Unable to create child process: $!\n");
}

if (not $pid) {
   exec("$program < $temp_file");
   die("Unable to launch application: $!\n");
}

twirling_baton(
   0.250,  # Twitch every 500ms
   0.500,  # Poll   every 500ms
   sub { waitpid($pid, WNOHANG) != 0 },
);
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Update: Oops, I used : instead of ? in min and max. Fixed.