FSDO got back to me:
Hello Mr. Frederick,
Thank you for your question. Regardless of the ratings the tailwheel student holds, A Sport Pilot instructor can only give the endorsement in a Light Sport airplane, but it’s valid for any tailwheel airplane that the holder is authorized to fly.
See AC 61-65H - Certification: Pilots and Flight and Ground:
A.71 To act as pilot in command in a tailwheel airplane: § 61.31(i). This endorsement may
be given in a sport pilot aircraft by a sport pilot instructor, or in an airplane by a flight
instructor with a rating other than a sport pilot rating.
I certify that [First name, MI, Last name], [grade of pilot certificate], [certificate number],
has received the required training of § 61.31(i) in a [make and model] of tailwheel
airplane. I have determined that [he or she] is proficient in the operation of a tailwheel
airplane.
Please call if you have any further questions.
Sincerely,
[redacted]
FAASTeam Program Manager (Temp) – Operations
Grand Rapids, FSDO
3196 Kraft Ave. SE, STE 103
Grand Rapids, MI 49512