I'm guessing the one you want to rewire is the same color as the machine so not black or white. I'm fairly certain that the one you want to rewire plugs into an outlet type plug. I know you would like to rewire the one that is on the machine, but if worse comes to worse, one could get a LED light or strip lights that is adjustable like one of these
https://www.amazon.com/sspa/click?ie...0aWM%26psc%3D1
https://www.amazon.com/sspa/click?ie...0aWM%26psc%3D1
https://www.amazon.com/POWKER-Magnet...s%2C198&sr=1-4