I want to run two of these...

Bicycle turn signal and brake light

off of one controller switch.

How do I raise the controller's voltage capability?

I ask this because I don't want to burn out the controller board, due to the batteries being stored in the light module.

 

You might ask the manufacturer.

Is the control you need all accomplished by hitting that one switch? You might be able to hack the second unit to respond to the switch on the other. It would help to have schematics or at least photos of the circuitry.

 

Well, if the problem is too much voltage in the batteries, a zener regulator could drop the voltage to a safe level. If however, you plan on running two lights from power flowing through one controller, you are going to run into power dissipation problems (Too much draw) or v-drop problems down the line. One way around this is to simply use the controller to switch power transistors on (as a "bypass") to handle the extra current draw.