I'm pretty sure scoping is not the issue (I thought this at first), because the following code works as expected:

$SIG{'INT'} = 'Int_Handler';
sub Int_Handler { $file = 2; };

$| = 1;
$file = 1;
while ($file) {
    print $file;
    $file = $file == 1 ? 1 : 0;
    sleep(1);
}
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While the OP should probably adhere to strictures (and is doing a lot of work inside a signal handler), this is not the issue.