While it has nothing to do with the problem you are experiencing, there are some oddities in your code. I wonder if there are reasons why you are doing them.

my $mytime = (time);
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time() returns a scalar, which you are assigning to a scalar. Why do you place it inside a list? Invoking array context makes no difference in the return value. Or were you intending to have the parentheses at the end, indicating a function call with no parameters, as in

my $mytime = time();
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if ($FileStat = (stat $File)[9]){
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Why do you have the stat return value as the condition of an if? Or was that part of your debugging, trying to figure out the odd results you were getting. I would suggest verifying each file exists, if you have any doubt or want to be robust, and then confidently and boldly getting and using it's mtime.