LII and EII do indeed seem to be the most common suggestions (including MBTI equilavents). I am currently favouring LII of those two, because his writing is full of crystal clear decisive logic, and is very much similar to the writing of LII philosophers such as Immanuel Kant and René Descartes. (Blaise Pascal might not seem so "logically-sound" by modern standards, but he perhaps has a similar style). I believe many historical EIIs may appear similar in style in terms of emphasizing their philosophical ideals, but in Jefferson's case, there does not seem to be any media (whether in speeches, letters, Declarations of Independence, novels etc.) where he displays anything that may seem more indicative of over (he seems generally quite "hard-nosed" albeit idealistic).

It is difficult to consider other types as possible on the evidence available (I do worry with historic people that certain types (e.g. LSEs...SEIs...ESEs) are disproportionately underrepresented for various reasons), although I am fairly certain he was an introvert. I should say that, after having argued for LII based on the lack of any obvious evidence of a stronger case for EII, I nonetheless strongly identify with his style and philosophy despite self-typing as EII. But again, I see no obvious sign of him being EII over LII.