The problem is with the HVAC black box underneath the cowl cover as mentioned three threads up. That black box below the cover consists of two plastic pieces, an upper one and a lower one that are attached and sealed with foam tape at the factory. The foam tape breaks down and the leaks begin. The problems is with getting good access to the box in order to repair the problem. LMG actually sells a replacement seal but I have yet to find a good way to make the fix that doesn't require tearing the dash apart. I have a '95 Z-71 and a '96 Suburban that both leak here. It drives me insane.
I pulled that foam tape out an siliconed on the inside an what I could reach on the outside of that joint. I removed the hood for better access, I put two coats of silicone on the inside an then siliconed that cover back over it. So far no leaks since an I didn't remove anything from the interior....