Well, thanks for the suggestions and to this forum. I found and fixed the problem!!!
First off, I located the service manual for my car on this site which was invaluable for understanding the workings of the DRL
http://www.nicoclub.com/FSM/G35/Sedan/2004/
This, along with the comment above, helped me zero in on the likely culprit - the "Daytime Light Control Unit" (and to find it in the engine compartment).
A couple of taps on the unit caused the headlights to flicker, so that's got to be a good sign that the problem is there.
A call to the local stealer - $270 for a replacement. Ouch. A call to the local auto wreckers - no G35's. So back to the internet and search for Daytime Light Control Unit and there are a whole load of posts on the Nissan forums about the unit and cracked solder connections, and that it is not too difficult to find and repair. So I did ....
Here are a series of photos that show the steps. The research took 4 days, the repair took about 30 minutes.
Jeff
Here is the location of the unit in the engine compartment
A little closer after removing it (easy)
Now for the fun part - open it up. There are 4 small plastic tabs that can be moved with a small screw driver,
Here are the insides - pretty simple for $270!!!
And the backside with all the soldering. See the suspicious area?
And zooming in .... Yup, that is a cracked solder connection. I applied some more solder with a soldering iron, and it's good as new. Reassembled everything and put it back in the car. Yes!!!