Mel, has the sensor ever been replaced? My guess is no, since you still have a bulb in the holder. In the '85, there is an O2 sensor dash bulb that is actuated by the odometer at approximately 60K miles. It's a non-resetable switch, so the service manual instructions are to "remove the bulb" which is somewhat akin to my favorite practice of cutting a piece of electrical tape to cover a glowing "idiot light" but I digress . . .
The Bosch O2 sensor at the dealership will run you over $100, BUT, if you search here you'll find out that the Ford Mustang 5.0 uses the identical Bosch part (you'll have to splice your own wires and use heat shrink tubing) for under $50 at the local FoMoCo parts place. Or, Oxygensensors.com has a full kit with a non-Bosch sensor for $50.
If you know which end of a wrench or ratchet does the work and can get under the car safely, it is a DIY job, much like swapping out spark plugs (remember to use anti-sieze compound)
One feature of the '85's CSI fuel injection system is that if the electronics (the computer connected to the sensor) fails, the system defaults to mechanical mode. The engine will run really rich and you'll notice it, but you will be able to drive the car safely.