Update: the little rubber t-pipe was so old and brittle that it split when I went to put it back on. So I gummed it up with a bunch of silicone bathroom caulk (didn't have any RTV sealant handy) stuck it back on, and gave it a few hours to set. I dont have power in my garage and the hair dryer trick would have required a VERY long extension cord, so the next day I just left it sitting for a few hours with the headlights on, to encourage the moisture to evaporate.

It's been a few days now and the moisture is GONE. What a big difference a tiny rubber tube can make!

Seems like that part would be a good candidate for 3D printing if other people start to experience the deterioration of the rubber like I did.