Let’s get this clear: I am not going through Izumi’s fan service scenes at any length.
Poor Klaus. Even though he is one of the core Sanzen’in family members, the amount of screentime he gets is simply too little, even in an incident which he gets kidnapped. All he gets is three pages to protest, laugh and scream, and then he is out of our sight. This is in sharp contrast to Izumi, who gets lost in the Clock Tower and manages to trigger all sorts of traps. For that she gets six pages of crying, smiling and fan service. At the end of the day, my bet is that you would remember this chapter for Izumi more than Klaus.
And let’s face it, the only reason for this difference in their treatments is that Klaus is not the attractive 17-year-old which Izumi is.
So, we are led to the conclusion that all the traps that Izumi triggers, together with the general design of all the levels of the Clock Tower, originates from a trick which hides (or shows) the location of the key. The question is: who did this? The key in question unlocks the Saznen’in inheritance, whereas the Clock Tower, as part of Hakuou Academy, is a Tennousu family property. Who in the Sanzen’in family would have the power to order that the Clock Tower at a Tennousu family property be built in a certain – a very inconvenient for walking through – pattern?
Really, the only person I can currently think of is Mikado himself. I am not entirely sure if Yukariko is this influential at the Tennousu family, but seeing that she is “loved by the gods” and all that… well, it is smarter not to rule her out either.