You don't mention what OS you're using, and I don't actually know if this is an OS-dependent issue, but I do know that on any unix-like system, the file size reported by "-s" will reflect the recent growth of a file while it is actively being written to by some other process:

my $path = "dir/file_to_watch";
my $prev_size = -s $path;
while (1) {
    sleep 5;
    my $size_now = -s $path;
    if ( $size_now > $prev_size ){
        print "file grew as of ".scalar localtime().$/;
        $prev_size = $size_now;
    }
}
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