something change if put $|++; at the top of your code? I suspect yes.

Infact you are not printing newlines and the console is linebuffered. Instead of $|++; you can also modify 'print "$I "; ' into 'print "$I\n"; ' to get the expected output.

Look at these example and how the output come out:

perl -e "sleep 1 and print qq($_ ) for 1..$ARGV[0]" 3
1 2 3

perl -e "$|++; sleep 1 and print qq($_ ) for 1..$ARGV[0]" 3
1 2 3
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I suggest you to read suffering from buffering? a milestone read and also Perl Idioms Explained - $|++

Anyway you can do something simpler like:

sub my_sleep {         # no prototype
  my $Seconds = shift;
  
  print "Sleeping for $Seconds seconds ...\n"; # added newline
   
  sleep 1 and print "$_\n" for 1..$Seconds;

  print "done\n"; 
}
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L*