FWIW...when I took the MCI and received my CFI-AMEL/Instrument, the FSDO inspector I met with gave me a temporary certificate for exactly that, "Flight Instructor: Airplane Mutliengine & Instrument Airplane." Unfortunately, doing a certificate search on faa.gov, my permanent license--once mailed out--will have the CL-Thrust limitation added, making my MEI next to worthless.
I used my instructor experience in the EA-18G (a Superhornet variant) for the civilian conversion and cited examples NATOPS including several WARNINGS regarding limited rudder authority during SE operations in afterburner at high alpha. At some point in the process, the issuing inspectors ruling was overturned, thus adding a CL thrust restriction.
I too would be interested in how the FAA classifies CL thrust. Thanks in advance for any input.
Cubdrick