CFI-I signoff
You do need a signoff to take the CFI-I practical.
14 CFR 61.187 makes that clear:
(a) General. A person who is applying for a flight instructor certificate must receive and log flight and ground training from an authorized instructor on the areas of operation listed in this section that apply to the flight instructor rating sought. The applicant's logbook must contain an endorsement from an authorized instructor certifying that the person is proficient to pass a practical test on those areas of operation.
14 CFR 61.187(a)(7) sets forth the training required for the CFI-I:
(7) For an instrument rating with the appropriate aircraft category and class rating:
(i) Fundamentals of instructing;
(ii) Technical subject areas;
(iii) Preflight preparation;
(iv) Preflight lesson on a maneuver to be performed in flight;
(v) Air traffic control clearances and procedures;
(vi) Flight by reference to instruments;
(vii) Navigation aids;
(viii) Instrument approach procedures;
(ix) Emergency operations; and
(x) Postflight procedures.
Finally, as long as the applicant is adding-on the rating to his/her current CFI certificate, you do not have to be a so-called "two-year" instructor to sign off an applicant for the CFI-I. 14 CFR 61.195(h)(2) mandates that requirement only for initial CFI applicants:
(2) Except for an instructor who meets the requirements of paragraph (h)(3)(ii) of this section,
a flight instructor who provides training to an initial applicant for a flight instructor certificate must --
(i) Meet the eligibility requirements prescribed in §61.183 of this part;
(ii) Hold the appropriate flight instructor certificate and rating;
(iii) Have held a flight instructor certificate for at least 24 months;
(iv) For training in preparation for an airplane, rotorcraft, or powered-lift rating, have given at least 200 hours of flight training as a flight instructor . . . .
(emphasis added)
In other words, any current CFI-I can sign off a CFI-I applicant only as long as the applicant is adding the rating to his/her existing CFI certificate. If the applicant is seeking initial instructor certification as a CFI-I, the instructor training him/her and signing off him/her must be a "two-year" instructor.
I'm not a real fan of some of the "FAQ" sites. They provide some guidance but are never black-letter law. I would turn to
AC 61-65D for better guidance,
and write up the signoffs exactly as set forth on the AC.
Hope that helps some more.