my ($starttime, $isopen, $totaltime) = (0, 0, 0);
while (<TIMELOG>) {
   if (/open$/) {
      next if $isopen;
      $isopen = 1;
      $starttime = getseconds($_);
   }
   elsif (/hold$/ || /closed$/) {
      next unless $isopen;
      $isopen = 0;
      $totaltime += getseconds($_) - $starttime;
   }
}

##</code><code>##

@lines = <TIMELOG>;
push @lines, makefake(time(), "closed");
for (@lines) {
   # Same loop body
}