There's no mouse/joystick mode. I'd guess since you've replaced the CIAs and tried other mice that it's likely a fault (ie, cold solder joint) with the connector on the motherboard, or the line for left/right signal is damaged on the motherboard somewhere. Have you tried gently wiggling the connector to see if it will work intermittently? Could be all you need is to reflow the solder on those mouse port pins.
Hope that helps, and good luck!
P.S., it might be worth trying reseating all the custom chips (I forget which one handles the mouse ports now, maybe Paula?) in case you just have some corrosion on that one pin...
