Can MBTI be measured objectively? I'm trying to figure out how MBTI would be operationalized in scientific research.
How could one operationalize the different types, E, I, N, S, T, F, P and J?
How could one look at numerical measurements of individuals and say "That is an E"?

Is there any research on objective differences between the types (without using NEO-PI-R or other Big5 inventories as the objective reference)?
The main question here is "is there any scientific research into objective differences between people with MBTI types?" I suppose a second question is "does this research actually SHOW differences?". This is one aspect of the debate about the validity of MBTI, which is covered in other questions (e.g., this one).

There is not as much research as you might think, which is because most scientists avoid the MBTI. It is a commercial product (you have to pay for it) with poor reliability, which means that scientific psychology tends to use better-validated and published scales. This recent meta analysis includes MBTI as one of the "ipsative" measures, finding little validity for predicting occupation. This paper is similar and suggests that normative measures like the MBTI can predict GPA and job performance, although they do so less well than the Big Five. I haven't found any other studies looking more closely at behaviour, although given that some people consider the Big Five to subsume MBTI types, you could look for that instead.