I don't know if you have to have a hash of lists, but this could be solved using a hash of hashes. I couldn't find a .tsv file to try this out (but did try it on a .csv and it seemed to work).

while(<>){
        chomp;
        my @s = split /\t/;
        my $r_name = $s[0];
        my $seq = substr $s[9], 0, 12;
        $read2seq{$r_name}{$seq}++;
        
}

my @keys_with_2_unique_vals =
    grep 2 == keys %{$read2seq{$_}}, keys %read2seq;
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UPDATE: To account for the change in OP's post. (He wants keys where both values are the same) Change the grep line to:

my @keys_with_equal_pair_of_vals =
    grep 1 == keys %{$read2seq{$_}}, keys %read2seq;
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