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A photo of the wheel with the newly installed 3rd brake light installed, all bolted to the tire carrier on my Toys by Troy bumper. The center cap with its LED light is a nice fit in the wheel.
I found a couple of bullet type electrical connectors in my parts box. I crimped them onto the extended LED wires and plugged them into the two wires I previously disconnected from the old 3rd brake light connector. While not necessary, I also used a piece of heat shrink to cover the connections and ensure they stayed plugged together.
Be sure to leave adequate wiring length for the swing away tire carrier (if so equipped) to swing open without pulling on the electrical wires. You can use electrical tape or a cable tie (both are shown above) to secure the wire loom to the tire carrier/bumper as necessary. Having your wires flop around, getting snagged on the brush off-road, is not something you want to have to stop and deal with on the trail.
And finally, a pic of what it looks like when it is dark out and no flash on the camera. I thought it was interesting how the placement of the LED light and the contour of the wheel causes a ring of red light to occur near the edge of the wheel.
Well folks, that is it. I told you it was an easy....and it looks good too. A simple wiring project that provides an aftermarket tire carrier with a functional 3rd brake light.