You can either either ignore a signal instance or handle it, but not both. Only future signals will be affected by your $SIG{TERM} = "IGNORE".

use Time::HiRes qw( sleep );   # Optional.

print("Process Id = $$\n");
print("Start time = " . localtime() . "\n");

my $term_sig;

local $SIG{TERM} = sub {
   $SIG{TERM} = "IGNORE";
   $term_sig = 1;
};

# Sleep for 20 seconds. Ignore interruptions.
my $sleep_til = time() + 20;
for (;;) {
   my $sleep_len = $sleep_til - time();
   last if $sleep_len <= 0;
   sleep($sleep_len);
}

print("End time   = " . localtime() . "\n");

if ($term_sig) {
   print "Received TERM signal\n"
} else {
   print "Did not receive TERM signal\n"
}
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Tested:

$ 603944.pl
Process Id = 65138
Start time = Fri Mar  9 01:06:18 2007
End time   = Fri Mar  9 01:06:38 2007
Did not receive TERM signal
$ 603944.pl
Process Id = 65236
Start time = Fri Mar  9 01:07:00 2007
   $ kill -s TERM 65236
End time   = Fri Mar  9 01:07:20 2007
Received TERM signal
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