> whether there's any information gain from knowing a person's previous MBTI results for subsequent tests
That doesn't seem like the proper question. Specifically, it works only to predict future MBTI results, not anything further. That's fine for height and weight because those values are robust to small/moderate changes in value.
MBTI already has low predictive power about real-world content, and high sensitivity to change (on the margins; it also suffers from applying a clustered model to non-clustered data). So if retest reliability is anything less than excellent, I worry that our predictive power has been almost totally destroyed.
To provide a new analogy, this is like variance in number of fingers. The significance of 11 vs 10 vs 9 isn't proportional to magnitude, so we wouldn't accept "small" counting errors.
None of that says that "I'm an INTP" is meaningless, but I suspect that MBTI is no better, or even worse, than non-formalized personality summaries.