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I had this happening a couple months ago. I figured it was the voltage regulator in the alternator acting up. You probably will notice your voltage readings swinging wildly. You might try cleaning and retightning the connections at the alternator, battery and ground. I did this but the problem was still there. Mine cleared up on it's own after a few weeks but I think my alternator is probably on borrowed time. You can have the alternator rebuilt by an electrical shop. The price I was quoted ($60.) was less than the cost of a "lifetime" rebuilt unit that everyone seems to have problems with. The shop will install HD parts (diodes, bearings, regulator, etc).
Most likely your voltage regulator in your alternator is oscillating. With the engine running and the lights pulsing, unplug the connector on your alternator and see if the pulsing stops. If it does, your alternator is the cause.
From: 10.70 @ 124mph, Stock Bottom End @ 3620lbs, ECS Racing Team Member. The 1st NMCA LSX Index Rumble World Champion. 2011,12,13 Champion
Re: Lights pulsing (dppeaden)
I had the same problem with my 89. It was the plug on the right headlight. The plug was actually melting causing a bad ground. Hope this helps. I replaced the plug, respliced the wires to the new plug.
Same problem on my '90. I first replaced the alternator as the one I had was the original or a very old replacement. Slight improvement.
Next, I followed the smaller cable from my battery positive terminal (not the one to my starter solenoid) to the stack of wire terminals gathered on a stud located between the batteryand firewall. I removed and cleaned all of the terminals. I applied Permatex di-electric tune-up grease to protect the terminals form future corrosion. This provided an almost complete fix.
The complete fix was accomplished when I did the same for the five grounds attached to my frame rails in the engine compartment.
Start with the battery terminal connections. Disconnect them (negative first)
clean them using a wire brush and then soak them in a water/baking soda solution. Wire brush the the battery recepticals and charge the battery.
After the battery is fully charged reconnected the wires (positive first).
My car had the same symptoms you describe and cleaning the battery terminals on my car solved the problem. LOL.