Extending ikegami's (++) to account for vatheck's multi-state lightswitch ("there are multiple possible states of off and one possible state of on") by adding a "switching" state as one of the possible states defined -- quite arbitrarily and sometimes illogically -- as "off":

#!/usr/bin/perl
use strict;
use warnings;

my %start_time;
my %total_time;
while (<DATA>) {  # Or iterate through your array
   chomp;
   my ($time, $name, $state) = split /,/;   # Or better: Text::CSV

   if ($state eq 'on') {
      if ($start_time{$name}) {
         warn("$name already on at $time!\n");
         next;
      }

      $start_time{$name} = $time;

   } elsif ($state eq 'switching') {
      if (!$start_time{$name}) {
         warn("$name changing state at $time!\n");
         next;
      }

   } else {
      if (!$start_time{$name}) {
         warn("$name not yet on at $time\n");
         next;
      }

      $total_time{$name} += $time - delete $start_time{$name};
   }
}

for my $name (sort keys %start_time) {
   warn("$name never turned off!\n");
}

for my $name (sort keys %total_time) {
   print("$name was on for $total_time{$name} seconds\n");
}

__DATA__
10000,switchA,on
10001,switchB,on
10002,switchC,on
10005,switchA,off
10007,switchA,on
10012,switchC,off
10013,switchB,off
10015,switchA,off
10020,switchE,on
10020,switchD,off
10020,switchF,on
10021,switchF,on
10099,switchZ,switching
10100,switchZ,on
10101,switchZ,off
10089,switchY,on
10093,switchY,switching
10094,switchY,off
[download]

Produces:

switchD not yet on at 10020
switchF already on at 10021!
switchZ changing state at 10099!
switchE never turned off!
switchF never turned off!
switchA was on for 13 seconds
switchB was on for 12 seconds
switchC was on for 10 seconds
switchY was on for 5 seconds
switchZ was on for 1 seconds
[download]

  :-) This does make this binary-minded pilgrim wonder though: "Is vatheck controlling a "3-way" bulb?"

More seriously, depending on the nature of the auditing being done, it might be well to calculate the "on" duration (as of the time of reporting) for those switches which are "never turned off" by subtracting the time of their first appearance in the data, to the last time found for any switch.