had an intermittent problem with mine on my XJ
It turns out it seemed to happen during car washes and when damp / raining.
As you so rightly say, the cabling around the rear diff area was chafing and the moisture caused short circuits or something I believe, never happened when it was dry........that was around 2 and a half years ago.
Whilst I was in at my local Indy for some other work he checked and found the chafing, he simply used electrical tape or similar and re sealed the chafed area and I've had no problems since......a quick and cheap n cheerful solution
Might be worth checking out if / when you can?
MY2008 ( 58 ) XJ X358 2.7 Tdvi Sovereign LWB remapped to 245bhp, Black, Ivory leather interior with black piping, 20" Alloys
MY2007 Audi A6 3.0 Tdi SE Quattro 176bhp Stratos Blue, Front & Rear park assist, Comms Pack High, Sline grille badge, 19" 7 twin spoke RS4 alloys,
Rear tints, Dipped bulbs 80W, Mainbeams 100W, Foglights 100W, Number plate bulb LED's, Interior bulb LED's, First Aid Kit