Ok, I know (less than) zilch about aeroplanes, so before I comment I need to ask.... do the electrical systems work like those in cars, where one half of the pathway is through the frame or other common return?- the so-called
earth?
Becasue if so, that may well be the problem here. A bad earth in a car (as opposed to a short... an open or not well made circuit, the opposite of a short (a
long 
) causes all sorts of funny symptoms. When one component is activated and there's a bad circuit, electricity gets a bit like water and finds its own way round, sometimes routing through other parts with strange results.
So yes, the suggestion to check the wiring is a good one... don't just look for short circuits (eg frayed wiring accidentally connecting to other parts, wires accidentally clamped where the insulationg might possibly be broken (but usually not all that apparent); look for open or poorly made circuits too (eg loose connections, or wiring tabs screwed to components where there might be paint preventing a good connection). In any case, a poor connection that might be arcing can cause all sorts of radio interference I think.
HTH?
Jim