It's difficult to solve because the clicking noises can be caused on both sides of the windshield.

If you have not already done so, try temporarily removing the plastic cowl that sits under the windshield wipers. My post explains how to do it. Take it for a drive, see if makes any improvement.

 

You could, you would need a few items and might run you a pretty penny, at that point it would be better to sell and add money to buy 2007+ GS350.

 

I am having a hard time removing it, once the windshield wipers are out, two plastic pieces on the right and left side removed. I noticed 2 clips in the fender holding it down ( probably clips because who ever replaced my windshield lost screws or original clips) removed those. Noticed 3 big in clips around the windshield, Have a hard time removing them.

 

I wouldn't buy another Lexus at this point if you put a gun to my head. We shouldn't even have to be discussing oil burning engines. They failed, massively with the GS 300. And now I'm paying the price. $6,300 to be exact.

 

The 2006 cowl was eventually redesigned, so maybe it's different in your newer model. The attached is from the 2006 manual. Just the 2 round retainer clips.

Might need to search for a newer diagram. For example, here's a website showing the cowl for a 2007 GS: Link.

 

so how exactly does the styrofoam sound come about? the cowl shakes and rubs the glass?

 

Yes. As the body flexes, the plastic cowl moves against the glass, and IIRC some metal bits on the firewall. If you remove the cowl but the noise remains, it's from somewhere else. If that eliminates some or all of the noise, then see if there's a revised part (I've seen 3 different part numbers for the 2006 over time), or can try insulating the points of contact.