Jukeboxes are amazing machines. Long before the invention of the transistor, or any digital microprocessors, these things existed, and did their job quite well! An amazing amount of electronics engineering went into these things to make them do their thing. The level of expertise that went into designing something like a jukebox from that era is something I cannot fathom.
I know if I needed to design a control system to operate a jukebox now, the task would be rather simple. Just pick a variety of programmable chips on the market, write a program of a few KB, and connect it up to the approperiate input and output devices...a few switches and relays, and you're all set. Back in the 50's though, all that stuff had to be Hard wired with discrete components!!!