What is the GEM module and will it cause you to get false readings from the information panel?

The place to start is by having the charging system professionally load-tested for maximum output current and "ripple" voltage. GM has had a huge problem with their generators since the '87 model year. If one diode fails of the six, system voltage will go low at times, and computers are very intolerant of low voltage. All of the warning lights you mentioned are run by their respective computers. The instrument cluster is now a computer in itself too. They will do weird things and may shut down intermittently. If the generator proves to have a problem, you can reduce the high number of repeat failures by replacing the battery at the same time unless it is less than about two years old.

Forgot to mention, the "GEM" module is "generic electronic module". That's Ford's name for their Body Computer. On GM vehicles, the engineers cleverly built the Body Computer into the radio so you have to get it fixed through the dealer's two grossly-overpriced repair centers.