Actually,
The Blueshawk, and Lucille, and other VariTone guitars have one (or two) inductors, and five (or ten) capacitors to make 5 LC tanks, plus no effect, for six settings.
If you look at how they're in the circuit, its easy to see that the sole reason for the 10m resistors is to keep the caps "charged", which makes them not "pop" after periods of disuse.
The 100k resistor is a load balancing resistor. What it does is makes sure you've got some load to counter the load of the LC tank. If it weren't there, the effect would be greatly diminished. Why? Because the LC circuit is a higher impedance than the pickup and the natural order of things would just have the electrons not go there. By putting in the resistor, it guarantees that the signal will detour throu the LC tank(s).
The value of the load balancing resistor will vary, according to the impedance of the L in the LC circuit... and to a lesser degree the ESR of the C. L=coil, C=capacitor
The excellent humbucking inductors from Lawrence are so low an impedance, that you don't need any load balancing resistor at all - or in fact - a sort of reverse load balancing resistor in most guitars. Whereas the Gibson inductor well beyond the impedance of most pickups, the Lawrence one is a mere 55ohms impedance. Transparent!~
By varying the inductance of the coil - the degree of high frequency retention is altered. Lower inductance preserves very high frequencies, while raising the inductance preserves more lower frequencies. Something in about 2hy will just start to get into the 2nd harmoncs. Going into 4hy will give upper fundamental frequencies - all dependent on the pickups of course. The capacitor preserves more and more lows. Bigger caps = more lows, smaller fewer lows. So, what Gibson has done is more or less got a variable low cut filter going on. It works well.