This sounds like a job for the evil 'goto'...

use strict;
use warnings;

open (T1, "t1") or die;

my $line;
my $flag = 1;
my $counter;

DATA:
while (<DATA>) {
    print;
    goto T1;
}

T1:
while (<T1>) {
    print;
    goto DATA;
}

__END__
file1
file1
file1
file1
[download]

This prints...

file1
file2
file1
file2
file1
file2
file1
file2
file2
file3, kidding... file2
[download]

Ira,

"So... What do all these little arrows mean?"
~unknown