Step 2: Modify your lights
This means you need to add a "+", a "-" and a "switch" terminal to the lights' circuits and wires to those to come out of the light's enclosure.
I don't have very good pictures of this, but it would depend on your light anyway.
Generally you can just attach the "-" wire in somewhere near the "-" of the battery compartment. The "+" and the "switch" are a bit more tricky, since you actually need to interrupt the circuit inside the light.
For the front light, I ended up making a disk with metal duct tape cut into appropriate shapes on each side. One side lines up with the battery terminals, and the other with the contacts on the lamp part. The "-" side goes around the disk to connect to both the lamp and the battery side. The "+" side lines up with the "+" of the battery. The "switch" lines up with the "+" contact on the lamp side that would usually line up with the "+" on the battery.
The back light I was able to take apart enough to solder the "-" right onto the battery cradle. I unsoldered the "+" side of the battery cradle from the lamp cicruit and soldered one wire onto the battery cradle and one onto the previously unsoldered wire.
In both cases, test the light after the circuit modification to make sure that the light will run on when the battery is attached while "+" and "switch" are touching. That is, make sure your light defaults to "on". If it does not, you may be able to mess with the circuit further, or you might need to get a different light. Or you could just skip the buckle part I will explain later and switch your light on as you did before.
If the lamps default to "on", find a way to get the wires out of the lamp cases while keeping the cases as waterproof as possible. I went through the rubber membrane that used to protect the switch on the back light. On the front light, where the lamp part screws onto the battery compartment, I filed a recess that the wires can sit in.
You'll need to see what works for your lights.