Judah wrote
Admittedly, before this thread started, I was not aware that ASEL
rating on a Flight Instructor certificate was not a prerequisite for
the Instrument rating, like on a Private Pilot certificate. That being
said, I don't think my lack of this particular knowledge was caused by
the use of the term CFI vs. CFII. However, it probably would have been
clear if the typical discussion included 3 distinct abbreviations:
CFI-A, CFI-I, and CFI-AI.

One of my points exactly!
However, there is no Land/Sea (ASEL) rating on the Flight Instructor
Certificate, and it would be CFI-IA instead of CFI-AI. As a matter of
fact, it would have to be either CFI-IA, CFI-IH, or CFI-IP

Bob Moore