Welcome Aboard!
First, best wishes to your mother.
As for the question at hand, the '13' will likely resurface once the engine is at operating temperature and the ECM is in closed loop mode. You can (and should) check the connection to the OČ sensor, but there is also a chance that the sensor is contaminated or weak. The '88 used a one-wire, non-heated OČ, and those tend to have a shorter service life. Fortunately for you, if the sensor is weak, a replacement can be had for about $20. The fuel savings alone can quickly pay for that. If you're lucky, it may only be a fouled connection.
You are correct that some of these engines can lose the magnet from the cam sprocket after time. That can be checked reasonably easily with a bi-directional scanner or a reasonably fast voltmeter or oscilloscope, since a missing magnet would mean that a CMP signal would never be generated. If using a scanner, even if the signal is "missing" it is best to verify that with a meter or 'scope, since the scanner is only reporting what the ECM sees, and not a direct reading from the sensor. If the signal is weak or intermittent, that would indicate that the magnet is likely intact. Magnets can be replaced, but that requires removal of the cam sprocket (no fun). An intermittent signal can be caused by contamination on the sensor face, contamination on the magnet, poor connections, or an electrically failing sensor.
The ignition system on your '88 may be the early version of the Buick "Fast Start" system. With this scheme, the engine will start and run with a bad CMP sensor, but usually after protracted cranking. The fuel system will run in batch fire mode as well. With an intact array of sensors, the engine should fire and run within one crank revolution, and usually considerably less.
The misfire error could be related to either the OČ or the CMP (or both). Solving the CMP sensor problem may clear that, but probably won't eliminate the '13' error. Lacking an OČ sensor signal, the ECM will revert to Backup Fuel Mode, which is typically rich (about 13:1). The ECM may also be limiting ignition timing as a result of a lost sensor signal, causing even less performance and mileage.