Not sure what city you live in, but the ad on the top of the cab is not "the light". I can't imagine a fare system that is not hooked directly to the actual "driver is available for a fare" light, i.e., once the fare is underway, the light switches off. Also, there are apps now in several cities to hail cabs, and some cab companies have their own apps (kind of like Uber, i.e., you can't hail a Lyft or Via via Uber, so why should there be a universal app to hail any cab -- but that would depend on your city and how cabs operate).
Yes, I've tried the one app that I've seen available here (Boston) but it didn't work. It's been a few months, I'll try it again. Cab drivers here don't use their available light so that they can't be ticketed for not picking up minorities.