A humbucking pickup has two coils: IIRC, the poles face in different directions relative to the strings. Also, the coils of wire are wrapped in opposite directions.
My question is severalfold:
must both coils be in proximity to the strings (I figure not)?
can the second coil be made smaller but somehow be compensated so that the same humbucking effect is produced?
can the second coil be placed elsewhere in the circuit besides connected to the first coil?
If the answers are no/yes/yes, I’m thinking that a small outboard second coil could be used to kill hum in a vintage fender without altering the guitar. Just think if you could locate the second coil in the plug of your guitar cord, you’d keep your guitar stock but kill the hum.
must both coils be in proximity to the strings (I figure not)?
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No. In fact, you can stack them vertically (as opposed to traditional humbuckers, which are side-by-side) and still kill the hum. DiMarzio makes a line of vertically stacked pickups for Stratocasters and similar guitars that buck the hum while retaining the sound and look of a single coil pickup.
I don’t know on this one, but my guess is yes. I think Actodyne General’s Lace Sensor pickups (used as stock Strat pickups for a while in the 80s and 90s) work on this principle.
I’ll be excited to hear what you come up with. As a dedicated Les Paul slinger, I won’t be personally affected, but it’s a very cool approach to a very old problem - that damned hum.
