All these years I assumed that Dear Prudence was the Rick, but hearing it in isolation I would testify in court that that is a Fender Jazz bass. It's both pickups, all knobs up all the way, bridge cover (with neoprene rubber mute), the stock Fender F80 flats, just like from the factory.
The "sonic fingerprint" of any guitar or bass is cemented by the physical location of the pickups, even more than what the pickups actually are. If you put two J pickups into a Rick, but maintained their original (Rick) position, it would still sound like a Rick. If you took a J bass, and relocated the pickups to where Rick places them, it certainly would not sound like a J anymore. So I would bet a large amount of money that this is the J. I'm kinda shocked actually.