I have encountered these kinds of strange electrical problems in both of my Series III XJ6s. In both cases replacing the ignition switch fixed it. This is the electrical switch that is connected to where you put the key into to start the car up. The Jaguar part number is DAC1607 and the Lucas part number is LU-35315. I just answered another poster who is also encountering problems, look up the thread called “Ignition with lock cylinder“ and search the archives for “ignition switch” and you will find many posts about strange electrical problems that were due to failing ignition switches. This is a common problem. In the case of my 1984 XJ6 Vanden Plas I believe it was due to the modifications made to the ignition switch wiring when aftermarket electronics were added to the car and caused the ignition switch to overheat. In the case of my 1987 XJ6 Vanden Plas it was just due to age and use.