Hrm... Well, one initial notion I have is along the lines of this: Rationality training should improve how good one can become at other stuff, or at least improve ability to gain skills/etc in other fields.

So, maybe tests could be something along the lines of find various subjects/fields a student is unfamiliar with and basically assign them to "get some knowledge and skill in this field."

How efficiently students can basically bootstrap up into something they're unfamiliar with should vary with their rationality, right? So something like this may be a starting point.

(Yes, I can see a bunch of details that would need to be worked out, but seems to be that this notion may at least be somewhere to start for developing rationality tests.)