What year did commercial airlines start using a lighted seat belt sign?
The earliest reference to seat belt signs I can find is Scheduled Air Carrier Rules, 14 C.F.R. (1941)
§ 61.342 Seat belt sign. An aircraft shall not be operated in scheduled air transportation unless a suitable means for warning passengers to fasten seat belts is provided. [As added by Amdt. 129, CAR, Sept. 5, 1941, effective Oct. 1, 1941, and Amdt. 130, CAR, Sept. 12, 1941; 6 P.R. 4691, 4753]
The amendment appears in 6 FR 4753
It's unclear where the motivation for this regulation came from, but it is likely mentioned in the Civil Aeronautics Board's meeting minutes for September 5, 1941. Unfortunately it does not appear that these minutes have been digitized. The relevant records should be available in the National Archives RG 197.2.