You can use split to extract individual fields from a line. E.g. something like this:

...
my $match_count  = 1;
my $prev_bead_id = '';
my $out          = '';

while (my $line = <IFILE>)
{
    my ($bead_id) = split ' ', $line;
    
    if ($bead_id eq $prev_bead_id) {
        $match_count++;
    } else {
        if ($match_count == $duplicate_count) {    
            print $out;
        }
        $match_count = 1;
        $out = '';
    }
    $prev_bead_id = $bead_id;
    $out .= $line;
}
# for when there is no further line after the last pair in the file:
if ($match_count == $duplicate_count) {    
    print $out;
}
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Update: fixed boundary case bug.