If you define

{
    local $/ = '====';
    open local(*FILE1), '<', shift or die $!;
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then you can discard a first (empty) read, and get the header info and data in two further reads,

    local $_ = <FILE1>;
    while (<FILE1>) {
        my @header_data = header_extract($_);
        my $data = <FILE1>;   # second read
        my @data = data_extract($data);
        # ...
    }
    close DATA1 or die $!;
    redo if @ARGV;
}
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