It's also much simpler. Why didn't I think of that?

use IO::Select ();

sub socket_read {
   my $sel = IO::Select->new($socket);

   while (!$sel->can_read(60)) {
      print STDERR "Received alarm\n";
   }

   my $len = $socket->sysread($line, 1024);

   ...
}
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Reference: IO::Select