If the water is working its way down from the roof or a window, it's likely to be pretty dirty and nasty by the time it gets to the taillights, and would presumably have caused other trouble (like delamination or punky areas). Most likely IMHO is that it's just the light fixture.
If you caulk around the light, it seems to me best to leave the bottom edge alone so that any water that does manage to get in has some slight chance of escape. Drilling a weep hole is also quite reasonable and shouldn't create any new difficulties.
If it's any consolation, I had much the same problem on a car I used to own, and solved it by drilling holes in the bottom of the lenses once I got tired of the sloshing sound when I opened the trunk. (The lights in question were mounted on the trunk lid on that car.)