For those who are unaware, running rich means that your car isn't getting the right air to fuel ratio and is getting too much fuel or not enough air. On the other side of things, running lean means your car isn't getting enough fuel or too much air.
The way these codes would present themselves only when I was idling and then disappear lead me to believe that there was an incompatibility with my TPS sensor because I had worked on it in the summer and transplanted the part from a salvaged throttle body. It turns out that wasn't the case however. As I started to get the codes more frequently I began doing more cleaning experiments with my electrical connections, focusing largely on the mass air flow sensor (or MAF sensor). It always seemed like the cleaning had a temporary effect, but the problem would return in the same way.
The way in which the codes were presenting themselves consistently helped me rule out that the MAF sensor had actually gone bad, but a bit of research about it helped me pinpoint the problem. What I discovered is that there wasn't a solid enough connection between the pins of the MAF and the connector. I took the MAF out and then slightly bent the pins so that they'd be pressing harder against the connector. My Jag seemed to cough and wheeze a few times after this as it seemed to be recalibrating or working out a new ratio. You could smell that the car was running really rich when it started still, however the running rich codes had stopped popping up.
After a few days the car was back to normal without incident and was able to idle without throwing codes anymore. It was such a simple and straightforward fix that it only readdresses some of my biggest frustrations with this car and the necessity to keep the components under the hood as clean as possible. In any case, bending the pins on the MAF sensor worked!
I've highlighted where the mass air flow sensor is located above. It is only held in with a couple of screws and you can use electrical contact cleaner on the wires, but be careful not to touch them directly as they are very sensitive. The pins for the connector can be cleaned with a toothbrush and I bent them using a kitchen knife.