1992 Buick Century Ignition Module @ ECM

It's possible that both the ignition module and ECM are going bad, but it's unlikely they'd both go at the same time.

When an ignition module is faulty, it may not provide enough voltage or dwell time to the coil to keep the spark plugs firing effectively as r.P.M.'S build. And it could be an intermittent problem also.

Your E.C.M. Controls your fuel delivery. Though on your specific vehicle the ignition module does the work of firing your spark plugs, the E.C.M. Still uses that information (timing) to control the injectors.

If you don't trust that mechanics opinion, then you really should take to one who you will trust. Because they have thousands of dollars worth of test equipment that will tell them exactly what's wrong, why, and how to fix it.

If you'd like to tackle this job yourself, then remove the suspected problem parts, go to AutoZone or any major parts store, and ask them to test them for you. If they are equipped to do so, they'll usually do it for free.

What you don't want to do is remove/replace parts hoping to hit the jack pot. This hardly ever works, and gets pretty expensive.