Headlights and interior light pulsate when.

Have the generator load-tested. In particular, look at the maximum current output and "ripple". If ripple is very high and output is exactly one third of its rated output, it has a bad diode. Bad diodes and voltage regulators are very common with this design that showed up in '87 models. It's common to go through four to six replacement generators in the life of the vehicle. To reduce the number of repeat failures, replace the battery at the same time unless it is less than about two years old. Suspect just the battery if it's getting old and the generator is able to develop its full output, typically around 90 amps.