Con,
From your picture it appears that your car’s Prior Owner, or his shop, made some wiring modifications to the wiring to your ignition switch and covered them with electrical tape. I highly suspect that these wiring modifications may be causing your fuel injector problems especially because that White-Yellow wire provides an important signal to the EFI ECU. I personally would not drive that car with those kind of shoddy looking splices and recommend that you get a new replacement switch right away. The Jaguar part for the ignition switch is DAC1607.
According to the Jaguar Series III S57 Electrical Guide (a very handy document to have) the Purple-Green and Purple-White wires are part of the Seat Belt Warning buzzer system. It looks a prior owner disabled it by disconnecting these wires.
The DAC1211 is the Power Resistor that provides the ground to fire the fuel injectors when the EFI ECU commands them to fire. The Series III XJ6 Parts Catalogue is a very helpful document to own when trying to sort out parts and part numbers and the DAC1211 is found on page 2G07.
I have found that the S57 Electrical Guide, the Parts Catalogue, and the two owners manuals (the green one and white one) are all worth their weight in gold as far as taking a lot of the mystery out of working on these cars. I would not be able to keep my three Series III saloons running without them.
Paul