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I have serched and read through all the posts on the interior/dash light flicker issue. After troubleshooting I was totally convinced my 96 Lt1 CE had a bad voltage reg in the alternator. I replaced the alternator and I still have the flicker in all interior lights. When I hit the brakes they really go dim, all other times it just a rapid flicker. I have looked for a bad ground, but so far have found nothing. I saw the post on the bulkhead connector. I didn't find it around my battery on my 96, but maybe I was looking in the wrong place. Anyone have any other ideas or suggestions for what I might try?
With the engine running, unplug the alternator and see if the flickering stops. If so, its the alternator, new or not. If its not the alternator, then you have an unreliable connection to your electrics. Almost all of the power to the car goes through the ignition switch. The ign sw has 4 poles (individual switches), one is for the starter solenoid and the other three switch power to these circuits (in my 87 and probably in your 96): 1.radio and windshield wiper: 2. VATS, injectors ECM: gages fuse, turn sig/ back up, cruise, cluster: 3. a/c, cooling fan, power windows.
An analog meter or better, an oscilloscope can look at the voltage wiggle and it should show higher variation after the poor electrical connection. I recommend you look at the voltage wiggle at the battery positive terminal and compare it to the amount at the input wire to the ign sw. This will tell you it might be the firewall connector. Look at the voltage wiggle after the ign sw and if larger, the switch contacts are suspect. I doubt its a ground because the stoplight lamps do not share a ground with the interior lamps, but those lamps do share a common path from the battery, through the firewall connector and then the ign sw contact. There is a wire off the positive battery cable lug that goes to a fuse block (on 96's I believe), so that wire connection to the lug is suspect along with the fuse block and then on to the firewall connector and the ign sw.
I recommend you buy the electrical diagnosis service manual supplement as it has every electrical circuit, the circuits description, a picture of parts location and diagnosis for typical problems (but not lights flickering). Let me know what you find.