You can have a thumb rest installed wherever you want it, but a better idea is to work on using less pressure on your thumb. It should just barely touch the pickup for a reference, not push into it hard. I rest most often on the neck pickup on my Jazzes, but I also move my hand around alot to influence the tone, sometimes I don't rest on anything, sometimes on the side of the fingerboard for plumper tone.
The weight of my arm is supported by the bass body, not the pickup. Practice at not resting, and barely touching, it will come. Good luck.