Thanks Hoahai. I agree the turn signal isn't necessary with the audible horn chirp. And the double chirp at the last tire is an added bonus. For some strange reason, I'm glad you had the same experience as me with the light not flashing. Makes me feel like mine isn't the only car with that missing feature. It is possible the light flashed quick - but you'd never see it because you're bent over the tire letting air out. Good idea to do it at night next time just to satisfy my curiosity.Your experience is the same as mine: I could not see my turn signal flash either. I just followed the horn chirp as the signal to move to the next tire. The light might have flashed one time very fast. In the daytime, it might be not noticeable.
Any way, the horn chirp is good enough and the procedure is easy to follow. I would not be bothered about the turn signal. It is obsolete because the procedure already tells you what tire should be next. Though, next time I would do it in night time to see if it flashes or not just for curiosity