The way the light works is simple- when the two terminals are connected and then disconnected, the light turns on. Repeating the connection and disconnection causes the light to cycle through each of its power settings. If the connection is made and left on, the bicycle goes into hazard flasher mode. My connection will preserve all of that functioning.
All I am doing is outsourcing the connection from the stock, "push button" switch to a retro switch in the shell of the miller light.
At that point, I have the LED in the dish and the switch ready. I clipped the power cord of the LED shorter and mounted the battery connection head from the LED's cord into a hole on the bottom of the Miller shell. The hole had to be modestly enlarged. Glue and a snug fit secure the connector in the shell.
Finally, I reassemble the shell parts and mount the light.
The light is set up so you can easily remove the rechargeable battery without having to mess with the light. Just disconnect the battery, and take it to an outlet.
When you're ready to ride again, reconnect the battery and strap it into the lamp bracket on the bicycle. It fits nicely.