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On all of the Hondas i've owned, including my current one, the foam gaskets that seal the taillight to the body shrink and leak. That's probably what is happening here.

You have a few options. The cheap way is to get some bathroom silicone sealant and apply it to the mating surface between the taillight and body. The correct way would be to replace the gasket. Unfortunately Honda charges a ridiculous amount for it and it costs about the same to get the entire taillight assembly with gasket from TYC (aftermarket), which is about $30.

 

Home Depot or Lowe's has foam stripping for storm doors that's adhesive on one side - I used this and it worked great - less than $5, I think (?)

 

I would recommend just getting the new gaskets. I used sealants before and if I needed to remove the tail light it was a pain. I just bought a set of two gaskets for the taillights for 11 bucks on ebay. Oem parts to. For the long term its just easier to replace the gaskets. Hope this helps.

 

Are you positive its running down the side of the trunk like you show?

On the driver's side, down below the taillight, there's the one-way vent that allows air to leave the vehicle but shouldn't let air or water in. Mine was leaking, badly, and water was coming in from there.