The best answer depends on a number of factors:
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How do you want the pickups to be connected when they are all active? In series, in parallel, or each one to a separate amplifier input?
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What is the resistance of each pickup?
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Can we safely assume that the peak signal voltage from the pickups is not more than +/- 0.5V ?
3 x CD4066 quad switch ICs may be suitable, but their on-resistance is 270 ohms typical @ 5V and 25C, which may be too high in some configurations (e.g. if you connect the pickups in series and use the switches to short out the ones you want to disable). Another possibility is 12 x 2N7000 mosfets, which have a muhch lower on-resistance.