That looks like the wiring that goes to the pull handle solenoid. Be careful about tugging or poking around with a metal screwdriver when the machine is powered up, you can short something out and cause damage. Not sure why the speaker in the coin tray would make noise when this connector is wiggled, is it just a static sound? You can turn power off and disconnect this connector to see if the contacts are shiny and making good connection. But I think those wires are just for releasing the pull handle on the side of the machine after you've pressed BET MAX or BET 1 and machine is ready to spin the wheels. I've attached your photo after I brightened it a little so we can see it easier.
What have you decided to do about figuring out what boards are or are not working?