Rough Cold Start

I know that rough cold starts seem to be a fairly common problem. My car (87 300E) runs rough for less than 5 seconds, and runs fine after that. I had posted this problem a while back, and I was told that the problem may be with the spark plugs, and could even be the valve stem seals. I replaced the spark plugs (used the standard copper core) and that did not solve the problem. However, for the past few days I have been experimenting when I start the car. I have discovered that, if I turn on the lights, right after I begin to turn the ignition, the car starts without any rough running. Could this indicate a bad OVP relay, or some other electrical component? Any insight would be greatly appreciated.

Brian