it is a microphone connector, and was used at the time because
it is an airtight way to bring the contacts out, so it could be mounted
from the air chamber/bellows side
both Switchcraft and Amphenol made an identical series of these,
you can still find some around. Usually it was the screw connector
on one end of the cable and a 1/4 inch on the other side, though some
PA systems also used these for the inputs early through mid 20th century
before you waste time on a cable, look inside to see if the Mic's are
still there, and that the internal wiring isn't shot.. you may also be able to
find an adapter somewhere that screws on then a normal 1/4" jack
plugs in.. it is kinda long and in the way then, but they work
the red dot cap is just to protect it when not in use
the accordion looks decent too..
enjoy !