I have a recently purchased a 2001 LS430 (very similar to your GS430, except larger) and I didn't think I had the manual either. However, the car has two glove boxes which was a pleasant surprise to me and it was in one of them. Also, I guess you have already found the leather folder stored in the trunk on the passenger side which also has some manuals.
I went to Lexus.com web site and registered my Lexus and logged in to their support site. There I downloaded the navigation manual before I discovered that my car already came with one. The printed navigation manual is also sold by Lexus and available on Ebay.
Now for your question: From my limited experience, it seems that if you agree to the guidance system, your screen will flip back to the map from audio after a preset time. If you don't use the guidance, I think the screen will stay on audio or climate. In the set up menu, I think I saw a setting that controls this feature. Go into the menu or set up screens and look around and see what settings are available. I do this about twice a week and have not memorized where things are yet. Still learning.
Ok, I tried it and it worked. Thanks. I appreciate it. I'll check on downloading that navigation manual too.
