Neat! I love reduced pattern BPs.
I may be wrong on this, but I seem to recall reading that genetic banded/genetic reduced is a simple dominant trait. So, you may not get a super, but it may still be simple Mendelian "genetic." (I believe it would be likely to be "genetic" either way, as we know it's possible to select for increasingly reduced-pattern animals, but I think what you're looking for is whether or not it's a single-gene mutation.)
I think that his daughter looking so much like him is very promising.