Chris,
Actually, EVERYTHING about these cars is logical -- it just isn't your logic!! (or any one else that owns them)
These XJ40s are notorious for having bad solder joints. It will happen all over the car and the blinker logic board is a prime example. If you are having problems after the car sat for 6 months and none of this was a problem previously, then get a solder iron and simply re-flow the solder on the logic board and any other place there are solder joints you think may be affecting it. Usually, this will take care of the problem. You will find the same problem with your clock and your bulb modules.
Remember that this car is nearly 20 years old now. In 8 years you can start running classic/antique plates on it in most States and like any car of this age, stuff is going to wear thin on it.
Cheers