A little disassembly here, a bit of Dremeling there, a little soldering and presto! A crappy looking black plastic thing with a wirey red plastic thing stuck to it. Amazing, No?
More seriously though, I must give mad props to Gorilla glue. It's some magical stuff, like a cross between wood glue and expanding foam. I thought it was all a bunch of ape-related hype until I got some to glue cork grips onto bike handlebars (at Rivendell's recommendation) But the stuff really is pretty awesome (for glue).
Back to the matter at hand, when I got it all slapped back together, here's what it looked like. I was a little worried that the LED trailer light wouldn't be bright enough in comparison to the rest of the brake lights, but I looked at it all lit up last night and it's fine. The only indication (in the dark) that it's not an OEM brake light is that it's relatively small at only 4" across.