, the OP posted a pic of that little electrically controlled valve that provides a vacuum path, as required for the active motor mount. It's part of the EMC (engine mount control) system. This part is common to all three Odysseys we've owned (2001 EX, 2002 EX, and 2003 EX).
It's rare that the front active mount on a Gen 2 Ody goes bad, but it's happened. We've had the occasional post where someone describes some "brown goo" that isn't motor oil, all in a puddle directly under that mount, like a molasses spill. That's a failed mount. Again, rare.
's question was about the hose that disconnected itself from the mount. His mount was fine, but he was searching for the point where it connects to the active front mount. It is not obvious at all where this hose nib is, hence the images I provided.