Well, seems like the rationality tests would be more similar to IQ tests than to personality test. Puzzles, time limits... maybe even the reaction times or lie detectors.

Yes, reaction times seem like an interesting possibility. There is an online test for racism which uses this principle. But it would be pretty easy to beat the test if the results counted for anything. Actually lie detectors can be beaten too.

Perhaps brain imaging will eventually advance to the point where you can cheaply and accurately determine if someone is engaged in deception or self-deception :)