Neither rule guess was correct.
Counterexample for each:
"AKHTBN iff it is the string PINEAPPLE" - GREAT is white.
"AKHTBN iff it has four or more vowels" - QUEUING is black.
White Koans
ELPPAENIP GREAT PINEAPPLE
Black Koans
APPLE BARBER LOOPING PINE
APPLEPINE INEAPPLE NANA PINEAPPL
BANANA LOOP NANNA QUEUING