I don't know that much and haven't had all that much experience diagnosing wiring problems so more informed opinions should get greater weight and consideration.
That said I'd start by checking ground connections at the battery, the big bunch of grounds behind the left middle cowling (oh that's ST1300; not sure if there is something similar on the 1100's), and wherever else there's a ground involved with the ignition circuit.
Has the bike been sitting a while? Look for mouse-chewed wiring, perhaps well inside the bike.
Any chance you've got a wire with abraded insulation, bumped up against something it should not be?
Any chance the wiring to / behind the key itself has corroded or come loose?
Any farkles that tapped the ignition-related wiring, at or near the fuses? Check those connections if so, and the taps themselves.
There you have it- the sum total of things I can think of, that my betters have discussed on various electrical threads I've read.