When I bought my S&S Nomad frame, it came with a cable splitter and I could not figure out where to install the splitter. Thanks for solving the mystery. It never occurred to me that the splitter could go between the brake arms on a V brake. I use cantilever on the back, I can remove the rear brake cable without tools by unhooking the cable yoke from the straddle cable, no splitter needed.
I do not recall, is the cable splitter threaded together or is it a quick release type of connecter? A century ago when most water and oil wells were drilled with cable tool drilling rigs, they used left hand lay cable on the rigs to avoid having their below ground drilling tools unthread during use. The constant tightening and loosening of the cable would loosen the fittings if a right hand lay cable was used, but a left hand lay cable would keep the tools threaded on tight.
On my S&S couplers, I wrapped electrical tape around each end of the S&S nut to keep dirt and crud out of the coupling. It also keeps it from unthreading. I have removed the tape a couple times to check that they were still tight and they were. The snow and slush in the photo really makes it clear how much crud the lower coupling is exposed to while riding.