If moving the lead to a different position affects whether or not you have spark, and you have changed the lead, it suggests the pickup. There is nothing else you can affect by moving the lead.
Damage inside the pickup wouldn't necessarly be visible, but might show up when you open and close an internal crack by moving the lead about.
The carbon inside the pickup can crack.
Is the base of the lead (where it screws in to to pickup) in good contact with the carbon block just below the threaded section?
There are a couple of things you can do to check.
Put the bike somewhere dark and either start it or kick it over. Watch around the pickup. You might see spark leakage.
If you have a multimeter, and the pickup out of the bike, you could test for continuity - or at least resistance. I'd try whilst moving the lead about, then between the carbon ends. A bit of Jiggling should show up any problems.
Nice looking bike by the way.
'51,'56 Squares, '48 VH, '27 Model C, R67/2, Mk IV Le Mans, '06 Super Duke and Ariel projects.