How do you replace the ignition lock cylinder on a 1990 olds cutlass supreme international

I agree. A little more in the way of diagnostics might save you a bunch of time and money. Find an experienced GM mechanic who understands the various relays, remote switches, linkages, lockout switches and whatever else may be a part of the ignition system. Hopefully such a person exists here somewhere and will chime in.

From what I'm able to find out, there is no ignition switch per say, but there is an ignition control module which I have yet to find its location. Also, I notice the digital dash flickers when the key is jiggled about which makes me believe there's something wrong in the steering column.

You could be right. However the ignition control module and other components like lockout switches etc are often located remotely at the base of the steering column and are connected to the ignition switch by long metal rods. The ignition key assembly's only function may be to move that rod. If you can have someone turn the key while you observe what is happening at the base of the steering column, you may be able to locate the faulty part. It will also help if you are a contortionist and have x-ray night vision capabilities. Things are pretty tight down there.