89 Pontiac Grand Am

Your car has a problem. The Service Engine Soon light is triggered by the car's computer, and is telling you that a sensor, or part is malfunctioning. The car needs to be scanned with an OBD scan tool, and that will tell you what the problem is.

Ouch, now I'm glad I asked. Someone said it might be my transmission. It had a part that malfunctioned - to slow the driveshaft or something when I came to a stop - they fixed it by unplugging it.

That could very well be what is causing the light to come on. You can't just go around unplugging sensors. If the car's computer detects one not working (or unplugged), it will trigger the light. Whatever problem you had needs to be fixed, not simply unplugged.