I think it's broken. AFAIK ALL vehicles by '88 had a buzzer or chime for the lights on or key in position. I had an '84 E-350 van that left the factory as a bare-bones cargo van that had a buzzer for the key and lights.
Some people like to rip everything out, but I like my truck to be idiot-proof I've never tried to diagnose a failure in this system, though, so I don't know how to go about it. I do recall hearing that, if you can find a modulator that chimes instead of buzzes, it's a straight swap...and it would be nice to do that someday