There are many ways to do what you want, one is

#!/usr/bin/perl
use CGI qw(:standard);
use strict;
use warnings;

my $var_username = param( "USERNAME" );
my $var_password = param( "PASSWORD" );

my $url="http://host.redirectdomain.com:9999/";
my $t=1; # time until redirect activates

print "Content-Type: text/html; charset=utf-8\n\n";

open ( FILE, "/tmp/password.txt" ) || die "The file could not be opene
+d";

my $didmsg=0; 
while ( my $line = <FILE> )
{
   chomp $line;
   ( my $username, my $password ) = split( ",", $line );
   
   if ( ( $var_username eq $username ) && ( $var_password eq $password
+ ) ) {
   print "$var_username, $var_password <br>"; # I will remove this in 
+real world
   print "Permission has been granted <br>";
   print "<META HTTP-EQUIV=refresh CONTENT=\"$t;URL=$url\">\n";
   $didmsg=1; 
   last; 
   }
   
   elsif ( ( $var_username eq $username ) && ( $var_password ne $passw
+ord ) ) {
   print "$var_username, $var_password <br>"; # I will remove this in 
+real world
   print "You entered an invalid password. <br>";
   print "Access has been denied. <br>";
   $didmsg=1; 
   last; 
   }

}
close( FILE );

unless($didmsg) {
   print "$var_username, $var_password <br>"; # I will remove this in 
+real world
   print "You entered an invalid username. <br>";
   print "Access has been denied. <br>";
   }
[download]

Notice the use of the $didmsg flag, and "last" to terminate the read loop early

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