The 4001S and 4001 have identical necks profiles...thin and fast! The 4001S belonged, for 30 years, to a VERY reputable luthier who has his own line of basses and stomp boxes. He got it from his close friend, who owns a boutique amp brand, who owned it since new. The bass builder said it's the best Ric Bass that he has come across in in almost 50 years. It really is a killer bass.
I was told that the 4005 is believed to be the only other factory finished Blue Boy 1960s Rickenbacker, besides the famous original ones done for Jim Reeves and his Blue Boys!! It is also the earliest known one, hence just the four knobs instead of the later five. It is factory marked inside the body as a "4001-I" John Hall refinished it during the run done for Japan, when Ric first revived the Blue Boy color for Japan only around 2002.
Both were real lucky finds!