More accurately, a 4001SB or an S with a Toaster-top pickup installed. When Rickenbacker first came up with the idea of Beatle lookalikes, they made the bass by simply taking off-the-shelf 4001S out of inventory and placing a Toaster-top pickup in the standard 1" position. When the 4001S were gone, they started making the 4003S, and with the Toaster, the 4003SB. Details on pp. 72-73 in the book. Note that this one on eBay has a set neck with the shedua strip, a positive identifier of production 4001S (and 4000) of the time.
When John Hall bought the company from his father, he stopped the B series lookalikes and replaced them with the more accurate V series starting in 1984.