Binding to a sequence of DNA that is a part of a type 2 promoter that controls transcription by RNA polymerase III. Type 2 promoters consist of an A box and a B box downstream of the transcription start site within the sequence within the sequence of the mature RNA. Type 2 promoters are found in many tRNA genes as well as in other small RNAs.
RNA polymerase III type 2 promoter DNA binding