Your insurance requirements may be stricter than FAA requirements, however.
I'd want a way more authoritative opinion than mine, but surprisingly it seems like you can do so.
§61.23 Medical certificates: Requirement and duration.
(a) Operations requiring a medical certificate. Except as provided in paragraphs (b) and (c) of this section, a person—
(3) Must hold at least a third-class medical certificate—
(ii) When exercising the privileges of a flight instructor certificate and acting as the pilot in command or as a required flight crew member, except when operating under the conditions and limitations set forth in §61.113(i);
Section C (VI) says:
(vi) Exercising the privileges of a flight instructor certificate and acting as the pilot in command or as a required flight crew member if the flight is conducted under the conditions and limitations set forth in §61.113(i).
61.113 (i) says
(i) A private pilot may act as pilot in command of an aircraft without holding a medical certificate issued under part 67 of this chapter provided the pilot holds a valid U.S. driver's license, meets the requirements of §61.23(c)(3), and complies with this section and all of the following conditions and limitations:
[basic med stuff]
You must have a commercial license and a medical certificate to get the rating.
Where is it written that you must have a medical certificate rather than Basic Med to take an initial CFI-Airplane practical test? Please review the 61.113(i) exception in 14 CFR 61.23(a)(3)(ii), which clearly says otherwise, and remember that per 61.47(b) the applicant is the PIC for the practical test flight.
Once you are current as a CFI/I, you do not even need a medical at all if your student can be PIC.
Richard....and are not required crew. Review the required crew rule. For that action you are safety pilot and that is a required crew member for the operation. Required crew is required to be current and medicaled, and typed if that applies). Basic does not cover required crew (it see 3rd class)....so you have to be very careful to massage PIC-legal as the trainee is PIC sole-manipulator.
I believe Bruce is talking about aircraft which require two pilots, like a Learjet. In that case, the CFI giving instrument training to the PIC is acting as the required SIC as well as being the safety pilot, and Basic Med doesn't cover someone not acting as PIC. A CFI acting as a required SIC as well as safety pilot would have to hold Third Class or better.