How do they mostly eliminate 60 cycle hum without also dampening intentional 60-ish cycle notes...?
Of course, pickups are coiled wire and magnets (signed, Capt. Obvious...).
Forget the magnets for the moment.
Any coil of wire, even a single loop, can be an antenna to receive outside signals, no magnet needed. And so it is with the coils of the humbucker receiving that bothersome external 60hz electromagnetic noise to create hum.
But each coil (each 'antenna') of a humbucking system is wound opposite of each other. (Commonly called 'reverse wound'). This puts the two coils out-of-phase, exactly opposite of each other. When the external 60hz noise hits the out-of-phase coils, two signals of opposite phase, but same strength, are generated by each coil. Signals of equal strength and opposite phase will cancel each other out, equaling 0 hum. Yay! No more 60hz hum.
So, up to this point, the coils have been an antenna configured to cancel outside gibberish noise.
Adding magnets now will turn those coils (with the help of vibrating strings) into a signal generator of bass notes. We already know the coils are wound out of phase to cancel outside noise, but the magnets are installed in each coil with their magnetic polarities reversed from each other (commonly called 'reversed polarity'). Reversed magnetic polarity puts each coil's string generated output into phase with each other. Signals of equal strength and in phase are doubled. Yay! Bass goodness, even 60hz (along with all the other freqs).
Can I get a "Huzza!" for the Reverse Wound/Reverse Polarity (RWRP) humbucker! LOL