One problem with old cameras is that chemicals leak out of the battery and corrode connections, which is what has happened here. So all I have to do is find the battery terminal and solder this wire back on. Or, replace the wire completely - which is what I ended up doing. So now, with the battery check light showing a happy green, I’d fixed the camera, right?
Wrong. The metering was all broken and the shutter didn’t open and close how it should. Turns out that my camera has succumbed to “The Pad of Death”. This is a thing with Yashica Electro 35 cameras. The shutter mechanism uses a tiny foam pad to transfer movement from one lever to another. But, plastic foam being what it is, after a while it turns to dust. No pad, no movement, broken camera.