As you are finding out, an intermittent fault is the hardest kind to nail down, precisely because it is not a constant condition.

I'm not favourably impressed by the news that your [u]new[/u] Gibson needed so much rework already. :eek:

Anyway, to the point. A humbucking pickup has two coils of wire. A 4-conductor cable simply makes both ends of each coil available for connection to your switches and such. Both coils should show approximately the same DC resistance on your meter. If you can't find the fault in the control cavity, then you will have to look at the pup itself. Unless the pickup has a cover on it, you should be able to inspect the connections. If it does have a cover, and you can't find any other culprit, you'd best put on your driving gloves.