Why not just read both lines at a time? It even seems to handle the case of the file ending with an odd line correctly.

#! perl -slw
use strict;

while( my $line = <DATA> . <DATA> ) {
    print "'$line'";
}

__DATA__
1   2   3
    4   5   6
1   2   3
    4   5   6
1   2   3
    4   5   6
1   2   3
    4   5   6
1   2   3
    4   5   6
1   2   3
    4   5   6
1   2   3
    4   5   6
an  odd  record
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