Check charging system and battery light on

How old is the battery? Was this a used or rebuilt generator that you installed? With the engine running, measure the voltage on the large output stud on the back of the generator and tell me what that is.

First you have to understand that starting with the '87 model year, GM went from the second best generator in the world, (my opinion), to by far the world's worst pile ever. If you installed a used one without knowing its history, there's a real good chance you got a bad one.

The thing that makes these such a poor design is they develop huge voltage spikes that damage the internal diodes and voltage regulator, and interfere with computer sensor signals. The battery is the key component in damping and absorbing those spikes but as they age and the lead flakes off the plates, they lose their ability to do that. The important thing to remember is to replace the battery at the same time as you replace the generator unless it is less than about two years old. That means, thanks to those harmful voltage spikes, your replacement generator might have been damaged as soon as you started the engine with the older battery.

The place to start is with that voltage reading. It needs to be between 13.75 and14.75 volts. You should find the exact same voltage at the battery terminals. If you do, the next part of the test requires a professional load tester. Your warning on the dash may be due to one failed diode of the six inside the generator. The output voltage might be okay, or even just a fuzz high, but the maximum output current you'll be able to get will be exactly one third of the unit's rated current. 30 amps from the common 90 amp generator isn't enough to run the entire electrical system under all conditions. The battery will have to make up the difference until it slowly runs down over days or weeks. The tester will also show "ripple" voltage which will be very high when a diode has failed. That is what is detected on a lot of newer cars to trigger the warning light.

It depends on the cause of the problem. Harbor Freight Tools has a perfectly fine digital voltmeter for less than ten bucks. You can also get a rough idea if the charging system is working by watching if the interior lights dim a little when you stop the engine.

Before you replace anything, as long as the battery is new now, have the charging system professionally tested. Some places will do that for free, but you don't want that done at an auto parts store. They don't do much more than that first half of the test that you can do yourself.