Interacting selectivity and noncovalently with a cyclic nucleotide mimicking protein motif that is part of the same protein. The CNBHD is a domain on KCNH channels that creates a binding pocket on the KCNH channel that resembles the cyclic nucleotide- binding domain on other ion channels. It binds to a peptide motif that is part of the same protein rather than a cyclic nucleotide.