Of course its electric.... so's my FiA master switch Never put any of them nasty pull cable things that get stuck and never work on our cars

Mark it makes no difference - just re-wire it like you would a bell or speaker.
Dont be tempted to cut and shut the wiring. Keep it 1 piece all the way from the plug to the switches too

May have some nice thin twin core somewhere knocking round the garage if your stuck.