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2nd Gen Ram Tech1994-2001 Rams: This section is for TECHNICAL discussions only, that involve the 1994 through 2001 Rams. For any non-tech discussions, please direct your attention to the "General discussion/NON-tech" sub sections.
I recently had to work on my brothers truck that had the same leak. I replaced that hose, made it a little longer, but put a caulking compound around the hole. From the way it looks, when the water drains from the stock output, it runs underneath the nipple rather than dripping off of it and goes through the firewall. The problem is probably exaggerated when your driving. The stock seal around the nipple was a type of foam rubber, and literally deteriorated when I touched it. I would put some inexpensive sealant around the opening where the hose meets the firewall, wait a few days to see if your problem still persist.