Hi Bill,
Call the factory. They might have been using the exact same LED 3rd brake light since they introduced the integrated spare tire wall in 2004. Make sure to mention it is for your 2005.
If you know how to use a soldering iron, you could remove, disassemble, and inspect the connections and solder joints for cracking or disconnect. Such an LED lighting fixture can sometimes be repaired. I have repaired some where I volunteer at an automotive charity.